A Sudoku grid is a 16x16 grid of cells grouped in sixteen 4x4 squares, where some cells are filled with letters from A to P (the first 16 capital letters of the English alphabet), as shown in the figure. The game is to fill all the empty grid cells with letters from A to P such that each letter from the grid occurs once only in the line, the column, and the 4x4 square it occupies. The initial content of the grid satisfies the constraints mentioned above and guarantees a unique solution.

b) Solution

Input

The first line of the input contains an integer K - determining the number of datasets (K<=10). Each data set encodes a grid and contains 16 strings on 16 consecutive lines as shown in the example input below. The ith string stands for the ith line of the grid, is 16 characters long, and starts from the first position of the line. String characters are from the set {A,B,…,P,-}, where – (minus) designates empty grid cells. The data sets are separated by single empty lines.

Output

For each data set in the input print the completed 16x16 Sudoku as specified by the rules above. The program prints the solution of the input encoded grids in the same format and order as used for input. The output for each data set should be separated by single empty lines.

Example

Input:

1
--A----C-----O-I 
-J--A-B-P-CGF-H-
--D--F-I-E----P-
-G-EL-H----M-J--
----E----C--G---
-I--K-GA-B---E-J 
D-GP--J-F----A--
-E---C-B--DP--O-
E--F-M--D--L-K-A 
-C--------O-I-L-
H-P-C--F-A--B---
---G-OD---J----H 
K---J----H-A-P-L 
--B--P--E--K--A-
-H--B--K--FI-C--
--F---C--D--H-N-

Output:

FPAHMJECNLBDKOGI 
OJMIANBDPKCGFLHE 
LNDKGFOIJEAHMBPC 
BGCELKHPOFIMAJDN 
MFHBELPOACKJGNID 
CILNKDGAHBMOPEFJ 
DOGPIHJMFNLECAKB 
JEKAFCNBGIDPLHOM 
EBOFPMIJDGHLNKCA 
NCJDHBAEKMOFIGLP 
HMPLCGKFIAENBDJO 
AKIGNODLBPJCEFMH 
KDEMJIFNCHGAOPBL 
GLBCDPMHEONKJIAF 
PHNOBALKMJFIDCEG 
IAFJOECGLDPBHMNK

Added by:	P.Kasthuri Rangan
Date:	2006-11-24
Time limit:	7s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	ACM Southeastern European Regional Programming Contest - 2006

SPOJ Problem Set (classical)

1112. Number Steps

Problem code: NSTEPS

Starting from point (0,0) on a plane, we have written all non-negative integers 0, 1, 2,... as shown in the figure. For example, 1, 2, and 3 has been written at points (1,1), (2,0), and (3, 1) respectively and this pattern has continued.

You are to write a program that reads the coordinates of a point (x, y), and writes the number (if any) that has been written at that point. (x, y) coordinates in the input are in the range 0...10000.

Input

The first line of the input is N, the number of test cases for this problem. In each of the N following lines, there is x, and y representing the coordinates (x, y) of a point.

Output

For each point in the input, write the number written at that point or write No Number if there is none.

Example

Input:
3
4 2
6 6
3 4

Output:
6
12
No Number

Added by:	Camilo Andrés Varela León
Date:	2006-11-25
Time limit:	2s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Asia - Tehran 2000

SPOJ Problem Set (classical)

1161. Tic-Tac-Toe ( I )

Problem code: TOE1

Tic Tac Toe is a child's game played on a 3 by 3 grid. One player, X, starts by placing an X at an unoccupied grid position. Then the other player, O, places an O at an unoccupied grid position. Play alternates between X and O until the grid is filled or one player's symbols occupy an entire line (vertical, horizontal, or diagonal) in the grid.

We will denote the initial empty Tic Tac Toe grid with nine dots. Whenever X or O plays we fill in an X or an O in the appropriate position. The example below illustrates each grid configuration from the beginning to the end of a game in which X wins.

Your job is to read a grid and to determine whether or not it could possibly be part of a valid Tic Tac Toe game. That is, is there a series of plays that can yield this grid somewhere between the start and end of the game?

Input

The first line of input contains N, the number of test cases. 4N-1 lines follow, specifying N grid configurations separated by empty lines.

Output

For each case print "yes" or "no" on a line by itself, indicating whether or not the configuration could be part of a Tic Tac Toe game.

Example

Input:
2
X.O
OO.
XXX

O.X
XX.
OOO

Output:
yes
no

Added by:	Camilo Andrés Varela León
Date:	2006-12-14
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Waterloo local 2002.09.21

SPOJ Problem Set (classical)

1162. Tic-Tac-Toe ( II )

Problem code: TOE2

In the game of tic-tac-toe, two players take turns marking squares of an initially empty 3 × 3 grid with either X’s or O’s. The first player always marks squares using X’s, whereas the second player always marks squares using O’s. If at any point during the game either player manages to mark three consecutive squares in a row, column, or diagonal with his/her symbol, the game terminates.

Given a board configuration, your goal is to determine whether the board configuration represents the possible final state of a valid tic-tac-toe game.

Input

The input test file will contain multiple cases. Each test case consists of a single line containing 9 characters, which represent the 9 squares of a tic-tac-toe grid, given one row at a time. Each character on the line will either be ‘X’, ‘O’ (the letter O), or ‘.’ (indicating an unfilled square). The end-of-file is marked by a single line containing the word “end”.

Output

For each input test case, write a single line containing either the word “valid” or “invalid” indicating whether the given board configuration is the final state of some possible tic-tac-toe game.

Example

Input:
XXXOO.XXX
XOXOXOXOX
OXOXOXOXO
XXOOOXXOX
XO.OX...X
.XXX.XOOO
OOXXXOOXO
end

Output:
invalid
valid
invalid
valid
valid
invalid
invalid

Added by:	Camilo Andrés Varela León
Date:	2006-12-14
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Stanford Local 2006

SPOJ Problem Set (classical)

1163. Java vs C ++

Problem code: JAVAC

Apologists of Java and C++ can argue for hours proving each other that their programming language is the best one. Java people will tell that their programs are clearer and less prone to errors, while C++ people will laugh at their inability to instantiate an array of generics or tell them that their programs are slow and have long source code.

Another issue that Java and C++ people could never agree on is identifier naming. In Java a multiword identifier is constructed in the following manner: the first word is written starting from the small letter, and the following ones are written starting from the capital letter, no separators are used. All other letters are small. Examples of a Java identifier are javaIdentifier, longAndMnemonicIdentifier, name, nEERC.

Unlike them, C++ people use only small letters in their identifiers. To separate words they use underscore character ‘_’. Examples of C++ identifiers are c_identifier, long_and_mnemonic_identifier, name (you see that when there is just one word Java and C++ people agree), n_e_e_r_c.

You are writing a translator that is intended to translate C++ programs to Java and vice versa. Of course, identifiers in the translated program must be formatted due to its language rules — otherwise people will never like your translator.

The first thing you would like to write is an identifier translation routine. Given an identifier, it would detect whether it is Java identifier or C++ identifier and translate it to another dialect. If it is neither, then your routine should report an error. Translation must preserve the order of words and must only change the case of letters and/or add/remove underscores.

Input

The input file consists of several lines that contains an identifier. It consists of letters of the English alphabet and underscores. Its length does not exceed 100.

Output

If the input identifier is Java identifier, output its C++ version. If it is C++ identifier, output its Java version. If it is none, output 'Error!' instead.

Example

Input:
long_and_mnemonic_identifier
anotherExample
i
bad_Style

Output:
longAndMnemonicIdentifier
another_example
i
Error!

Added by:	Camilo Andrés Varela León
Date:	2006-12-14
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Northeastern Europe 2006

SPOJ Problem Set (classical)

1166. Dead Fraction

Problem code: DEADFR

Mike is frantically scrambling to finish his thesis at the last minute. He needs to assemble all his research notes into vaguely coherent form in the next 3 days. Unfortunately, he notices that he had been extremely sloppy in his calculations. Whenever he needed to perform arithmetic, he just plugged it into a calculator and scribbled down as much of the answer as he felt was relevant. Whenever a repeating fraction was displayed, Mike simply reccorded the first few digits followed by "...". For instance, instead of "1/3" he might have written down "0.3333...". Unfortunately, his results require exact fractions! He doesn't have time to redo every calculation, so he needs you to write a program (and FAST!) to automatically deduce the original fractions.

To make this tenable, he assumes that the original fraction is always the simplest one that produces the given sequence of digits; by simplest, he means the the one with smallest denominator. Also, he assumes that he did not neglect to write down important digits; no digit from the repeating portion of the decimal expansion was left unrecorded (even if this repeating portion was all zeroes).

Input

There are several test cases. For each test case there is one line of input of the form "0.dddd..." where dddd is a string of 1 to 18 digits, not all zero. A line containing 0 follows the last case.

Output

For each case, output the original fraction.

Example

Input:
0.2...
0.20...
0.474612399...
0

Output:
2/9
1/5
1186531/2500000

Added by:	Camilo Andrés Varela León
Date:	2006-12-16
Time limit:	4s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Waterloo Local Contest Sep. 27, 2003

SPOJ Problem Set (classical)

1167. Move To Invert

Problem code: MINCOUNT

A triangle made of coins of height h is as follows
It has h coins at the base and h-1 coins one level above base and so on.(Coins are placed as shown in the figure below)
And at the top most level there will be only one coin
Now given h the task is to invert this triangle by moving minimum number of coins. For example when h=4 triangle is
Invert
For h=4 at least 3 coins must be moved to invert it.

Input

In the first line N will be given and then N lines follow with each line having a integer which is the height of triangle in that test case.00≤h<10¹⁰;

Output

For each test case output in a seperate line the minimum number of moves required to invert the triangle. Output fits in long long data type

Example

Inputt:
1
3

Output:
2

Added by:	Abhilash I
Date:	2006-12-16
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS
Resource:	IIIT Hyderabad Local Programming Contest

SPOJ Problem Set (classical)

1182. Sorted bit squence

Problem code: SORTBIT

Let's consider the 32 bit representation of all integers i from m up to n inclusive (m ≤ i ≤ n; m × n ≥ 0, -2^31 ≤ m ≤ n ≤ 2^31-1). Note that a negative number is represented in 32 bit Additional Code. That is the 32 bit sequence, the binary sum of which and the 32 bit representation of the corresponding positive number is 2^32 (1 0000 0000 0000 0000 0000 0000 0000 0000 in binary).

For example, the 32 bit representation of 6 is 0000 0000 0000 0000 0000 0000 0000 0110

and the 32 bit representation of -6 is 1111 1111 1111 1111 1111 1111 1111 1010

because

0000 0000 0000 0000 0000 0000 0000 0110 (6)
+
1111 1111 1111 1111 1111 1111 1111 1010 (-6)
-------------------------------------------------
= 1 0000 0000 0000 0000 0000 0000 0000 0000 (2^32)

Let's sort the 32 bit representations of these numbers in increasing order of the number of bit 1. If two 32 bit representations that have the same number of bit 1, they are sorted in lexicographical order.

For example, with m = 0 and n = 5, the result of the sorting will be

No.	Decimal number	Binary 32 bit representation
1	0	`0000 0000 0000 0000 0000 0000 0000 0000`
2	1	`0000 0000 0000 0000 0000 0000 0000 0001`
3	2	`0000 0000 0000 0000 0000 0000 0000 0010`
4	4	`0000 0000 0000 0000 0000 0000 0000 0100`
5	3	`0000 0000 0000 0000 0000 0000 0000 0011`
6	5	`0000 0000 0000 0000 0000 0000 0000 0101`

with m = -5 and n = -2, the result of the sorting will be

No.	Decimal number	Binary 32 bit representation
1	-4	`1111 1111 1111 1111 1111 1111 1111 1100`
2	-5	`1111 1111 1111 1111 1111 1111 1111 1011`
3	-3	`1111 1111 1111 1111 1111 1111 1111 1101`
4	-2	`1111 1111 1111 1111 1111 1111 1111 1110`

Given m, n and k (1 ≤ k ≤ min{n − m + 1, 2 147 473 547}), your task is to write a program to find a number corresponding to k-th representation in the sorted sequence.

Input

The input consists of several data sets. The first line of the input file contains the number of data sets which is a positive integer and is not bigger than 1000. The following lines describe the data sets.

For each data set, the only line contains 3 integers m, n and k separated by space.

Output

For each data set, write in one line the k-th number of the sorted numbers.

Example

Sample input:
2
0 5 3
-5 -2 2

Sample output:
2
-5

Added by:	Lê Đôn Khuê
Date:	2006-12-28
Time limit:	20s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	ACM ICPC 2006, Asia Regional Contest, site Hanoi

SPOJ Problem Set (classical)

1183. Accomodate the palace

Problem code: PALACE

There is a big palace in which rooms are constructed in the from of a square matrix.Now these rooms have to be filled with people.
As there are conflicts between people to maintain the equilibrium total number of people must be odd in every row and every column.
A room can accomodate only a single person.
Given the size of palace N one has to find total number of ways people can be accomodatede in that.

Input

First line consits of an integer K and then K test cases follow.

Output

For each test case you have to output the result%98777 in a seperate line.

Example

Input:
1
3
Output:
16

Added by:	Abhilash I
Date:	2006-12-30
Time limit:	3s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	IIIT Hyderabad Local Programming Contest

SPOJ Problem Set ()

1267. Origin of Life

Problem code: ORIGLIFE

Conway's Game of Life is not really a game, but a cellular automaton -- a set of rules describing interactions among adjacent cells on a grid. In our game, we have an n by m rectangular grid of cells identified by integer coordinates (x, y). The game progresses through a series of steps; at each step a new generation is computed from the current generation. The game begins with the first generation. In any given generation, which we shall call the current generation, each cell is either live or dead. In the next generation, each cell's status may change, depending on the status of its immediate neighbours in the current generation. Two distinct cells (x₁, y₁) and (x₂, y₂) are immediate neighbours if they are horizontally, vertically, or diagonally adjacent; that is, if |x₁ - x₂ ≤ 1| and |y₁ - y₂ ≤ 1|. Each cell that is not on the border of the grid has eight immediate neighbours. There are three integer parameters (a, b, c) which affect the game. The rules of the game are:

If a live cell has fewer than a live neighbours in the current generation it dies of loneliness. That is, it is dead in the next generation.
If a live cell has more than b live neighbours in the current generation it dies of overcrowding. That is, it is dead in the next generation.
If a dead cell has more than c live neighbours in the current generation it is born. That is, it is live in the next generation.
Otherwise, a cell's status is unchanged from the current generation to the next.

This process continues indefinitely. Eventually, a generation may be repeated in which case life goes on forever. Or all the cells may die. Similarly, if we explore previous generations that may have led to the current one, we may find one that is necessarily a first generation; that is, it could not have been created from a previous generation by following the rules. Such a generation is known as a Garden of Eden. Given the game parameters and the current generation, you are to determine whether or not the game might have started with a Garden of Eden. If so, output the number of steps necessary to reach the current generation from the Garden of Eden. If there are several possible answers, find the smallest. If there is none, output -1.

Input

Input begins with a single integer, the number of test cases. For each test case, there are m+1 lines of input in total. The first line contains the game parameters, which are five integers m,n,a,b,c each separated by one space. The constraints are 1≤m≤4, 1≤n≤5, 1≤a<b≤8, 1≤c≤8. The next m lines each contain a string of n characters representing a row of the current generation. In the string, an asterisk ("*") indicates live while a period (".") indicates dead. There are no blank lines between test cases.

Output

Output is one integer per test case denoting the minimum number of steps required to reach the input from a Garden of Eden. If there is no Garden of Eden, output -1.

Example

Input:
1
4 5 2 3 2
.****
.****
.****
.****

Output:
2

Output Explanation:

Assume the sample input is the "current" generation. A possible previous generation is

**.**
..*.*
....*
*****

The above generation can be derived from the following previous generation

.****
**.*.
*****
*..*.

This generation cannot be derived from any other generation. Furthermore, there is no shorter series of generations that has these properties.

Added by:	Bobby Xiao
Date:	2007-01-24
Time limit:	5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Canadian Computing Competition, 2006 Senior Stage 1

SPOJ Problem Set (classical)

1268. CN Tower (Easy)

Problem code: CNEASY

Christy C. Coder is traveling to Waterloo for a programming competition. On the way, she stops in Toronto to do some sightseeing. The unfortunate thing about travelling is that everyone back home expects her to bring back pictures of everything. Christy hates taking pictures: it makes her look like such a tourist! Fortunately, Christy has a plan to make her picture-taking quite painless.

At 553 m tall, CN Tower is the world's tallest free-standing building. 351 m up the tower is the "360" rotating restaurant, which rotates a full 360 degrees every 72 minutes. From there, Christy can see the whole city, and take close-up pictures of all the landmarks using her fancy new 100x optical zoom camera. Since the restaurant itself rotates, she only needs to stand in one place to take pictures in all directions.

The waiters insist that she order something or leave, and Christy is not interested in any of the items on the menu. Therefore, she must act quickly before she gets kicked out. Given the locations of the landmarks of which Christy wants to take a picture, your task is to determine the minimum amount of time that she must spend in the restaurant in order for it to rotate enough to bring all the landmarks in view. Assume that Christy always points her camera exactly perpendicular to the window to minimize distortion due to the glass. Note that multiple landmarks may occupy the same (angular) position, and these landmarks would only require one photograph to capture them.

Since the restaurant staff only realize she is a tourist once she starts taking pictures, we begin measuring the time required once she takes her first picture. Therefore, Christy can move to any position in the restaurant without hassle from the restaurant staff and begin taking pictures from there.

Input

The first line of input consists of the number of test cases. For each test case, the first line is an integer n (2 ≤ n ≤ 1000), the number of landmarks Christy wants to photograph. Each of the following n lines specify a landmark. Each landmark specification consists of the landmark name (a string of uppercase and lowercase letters of length at most 40 characters), a space, and the compass angle d, in degrees, to the landmark from the CN Tower (0 = north, 90 = east, 180 = south, 270 = west). Note that d is a real number which satisfies 0 ≤ d < 360, with d specified to the hundredth of a degree (i.e., at most two decimal places).

Output

For each test case, output a single integer, the minimum number of seconds that Christy must remain in the restaurant. If the time is not an integer number of seconds, round it up to the nearest second (i.e., take the ceiling of the number).

Example

Input:
1
5
CasaLoma 231.0
OntarioParliament 123.0
SkyDome 75.0
RoyalYorkHotel 340.0
PearsonAirport 165.0

Output:
3012

Added by:	Bobby Xiao
Date:	2007-01-24
Time limit:	2s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All
Resource:	Canadian Computing Competition, 2006 Senior Stage 2

SPOJ Problem Set ()

1269. CN Tower (Hard)

Problem code: CNHARD

The elevator normally takes 61 seconds to get from the ground up to the rotating restaurant. Unfortunately, when Christy arrives at the CN Tower, she learns that the elevator is out of service, so she has to take the stairs, which takes somewhat longer. Christy arrives at the top at 9:36 pm, by which time it is dark. She can only take pictures with a very powerful flash, which takes a long time to recharge between pictures. While the flash is charging, she cannot take any pictures. Thus, Christy needs a new program to calculate the minimum time that she must spend in the restaurant in order for it to rotate enough to bring all the landmarks in view, and taking into consideration the charging time of the flash. In addition to these difficulties, the restaurant closes at midnight. Thus, Christy may not have enough time to take pictures of all the landmarks.

As before, assume that Christy does not move around in the restaurant after choosing her initial position, but waits for it to rotate to the angle required to take each picture. As with the daytime problem (CNEASY), Christy can (very quickly) pick her initial position, since the restaurant is not that big. Christy always points her camera exactly perpendicular to the window to minimize distortion due to the glass. After taking the last picture, Christy must stay in the restaurant until her flash recharges. Since it is dark outside, if more than one landmark occupies an angular position, Christy can capture only one one landmark per photo (in order to keep the desired landmark in focus, blurring all others).

Input

The first line of input consists of the number of test cases. For each test case, the first line is an integer n (1 ≤ n ≤ 1000), the number of landmarks Christy wants to photograph. Each of the following n lines specify a landmark. Each landmark specification consists of the landmark name (a string of uppercase and lowercase letters), a space, and the compass angle, in degrees (specified with a maximum of 2 decimal places), to the landmark from the CN Tower (0 = north, 90 = east, 180 = south, 270 = west). Finally, the last line contains the amount of time, in seconds, required for the flash to charge.

Output

Example

Input:
1
5
CasaLoma 231.0
OntarioParliament 123.0
SkyDome 75.0
RoyalYorkHotel 340.0
PearsonAirport 165.0
10

Output:
3022

Added by:	Bobby Xiao
Date:	2007-01-24
Time limit:	4s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	Canadian Computing Competition, 2006 Senior Stage 2

SPOJ Problem Set (classical)

1270. Paint By Numbers

Problem code: PNTBYNUM

Years ago, there was a really bad craft/hobby called paint-by-numbers: you were given a line drawing, with numbers in each enclosed region, and the number corresponded to a particular colour. An example is shown below (unsolved on the left; solved on the right):

(images from ThisLife.org)

The problem you have to solve is much more linear, in a way.

You will be given an n-by-m grid (1 ≤ n, m ≤ 32) which you will "colour" in with either a dot ('.') or a star ('*').

Of course, the grid will not be specified in the usual paint-by-numbers way, since this would be too easy.

Instead, you will you have to infer which cells are blank and which contain a star. The only information you will be given are a collection of n + m sequences of numbers, one sequence for each row and column. The sequence will indicate the size of each continuous block of stars. There must be at least one dot between two consecutive blocks of stars.

An example is shown below (which is supposed to look fish-like):

You may notice that some paint-by-number patterns are not uniquely solvable. For this problem, you may assume that any solution which satisfies the specification is correct.

Input

Input begins with a line with the number of test cases. Each test case consists of a total of n + m + 2 lines. The first line of the test case consists of an integer n (1 ≤ n ≤ 32), the number of rows. The second line consists of an integer m (1 ≤ m ≤ 32), the number of columns. On the next n lines, there will be sequences which describe each of the n rows (from top to bottom). Each line will contain some positive integers, with a space between adjacent integers, and the sequence will terminate with the integer 0. On the next m lines describe the m columns (from left to right), the same format as the rows are specified.

Output

Output consists of n lines for each corresponding test case, each line composed of m characters, where each character is either a dot ('.') or a star ('*'). Separate test cases with a blank line.

Example

Input:
2
4
7
2 2 0
5 0
5 0
2 2 0
1 1 0
1 1 0
2 0
2 0
4 0
4 0
2 0
4
4
2 1 0
3 0
3 0
1 1 0
4 0
3 0
3 0
1 0

Output:
**..**.
..*****
..*****
**..**.

**.*
***.
***.
*.*.

Added by:	Bobby Xiao
Date:	2007-01-24
Time limit:	5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Canadian Computing Competition, 2006 Senior Stage 2

SPOJ Problem Set (classical)

1285. Continuous Fractions Again

Problem code: CFRAC2

A simple continuous fraction has the form:

where the ai’s are integer numbers.

The previous continuous fraction could be noted as [a1, a2, . . . , an]. It is not difficult to show that any rational number p / q , with integers p > q > 0, can be represented in a unique way by a simple continuous fraction with n terms, such that p / q = [a1, a2, . . . , an−1, 1], where n and the ai’s are positive natural numbers.

Now given a simple continuous fraction, your task is to calculate a rational number which the continuous fraction most corresponds to it.

Input

Input for each case will consist of several lines. The first line is two integer m and n,which describe a char martrix,then followed m lines,each line cantain n chars. The char martrix describe a continuous fraction The continuous fraction is described by the following rules:

Horizontal bars are formed by sequences of dashes `-'.

The width of each horizontal bar is exactly equal to the width of the denominator under it.

Blank characters should be printed using periods `.'

The number on a fraction numerator must be printed center justified. That is, the number of spaces at either side must be same, if possible; in other case, one more space must be added at the right side.

The end of the input is indicated by a line containing 0 0.

Output

Output will consist of a series of cases, each one in a line corresponding to the input case. A line describing a case contains p and q, two integer numbers separated by a space, and you can assume that 10^20 > p > q > 0.

Example

Input:
9 17
..........1......
2.+.-------------
............1....
....4.+.---------
..............1..
........1.+.-----
................1
............5.+.-
................1
5 10
......1...
1.+.------
.........1
....11.+.-
.........1
0 0

Output:
75 34
13 12

Added by:	Camilo Andrés Varela León
Date:	2007-01-31
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	HNU Contest

SPOJ Problem Set (classical)

1296. 4 values whose sum is 0

Problem code: SUMFOUR

The SUM problem can be formulated as follows: given four lists A, B, C, D of integer values, compute how many quadruplet (a, b, c, d ) belongs to A x B x C x D are such that a + b + c + d = 0 . In the following, we assume that all lists have the same size n

Input

The first line of the input file contains the size of the lists n (this value can be as large as 4000). We then have n lines containing four integer values (with absolute value as large as 2²⁸ ) that belong respectively to A, B, C and D .

Output

Output should be printed on a single line.

Example

Input:
6
-45 22 42 -16
-41 -27 56 30
-36 53 -37 77
-36 30 -75 -46
26 -38 -10 62
-32 -54 -6 45
Output:
5

Added by:	Abhilash I
Date:	2007-02-06
Time limit:	10s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	South western 05-06

SPOJ Problem Set (classical)

1325. Partial Sums

Problem code: PARTSUM

Given a sequence of positive integers a₁, a₂, ..., a_N, and 1 ≤ i ≤ j ≤ N, the partial sum from
i to j is a_i + a_i+1 + ... + a_j.

In this problem, you will be given such a sequence and two integers P and K. Your task is to find the smallest partial sum modulo P that is at least K.

For example, consider the following sequence of integers:

12     13     15     11     16     26     11

Here N = 7. Suppose K = 2 and P = 17. Then, the answer is 2 because 11 + 16 + 26 = 53 and 53 mod 17 is 2. On the other hand, if K = 0 the answer is 0 since 15 + 11 + 16 + 26 = 68 and 68 mod 17 is 0.

You may assume 1 ≤ N ≤ 100000.

Input

The first line of the input contains the number of test cases, T.

Each test case begins with a line containing three integers, N, K and P. This is followed by the values of a₁, a₂, ..., a_N, one per line.

Output

Output one line per test case, containing the smallest partial sum modulo P that is at least K, as described above.

Example

Input:
1
7 2 17
12
13
15
11
16
26
11

Output:
2

Warning: large Input/Output data, be careful with certain languages

Added by:	Stephen Merriman
Date:	2007-02-22
Time limit:	7s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Indian Computing Olympiad, Online Programming Contest, July 06

SPOJ Problem Set (classical)

1326. A Chase In WonderLand

Problem code: CHASE

Alice is in Wonderland. It is March and March Hare is raving mad. It begins to chase Alice. Alice runs as fast as she can, but she comes to the the edge of a quicksand pool. Now this pool has several safe spots where she may comfortably step on without being swallowed by the quicksand. She may step onto any safe spot from solid ground, but thereafter she can jump from spot to spot only in a straight line, and she cant turn back. March Hare is still hot on her heels, so she needs to know the maximum number of jumps she can make.

Input

On the first line there will be a single integer n, denoting the number of test cases. Each test case will consist of a single integer k by itself on a line, followed by k lines containing the x and y co-ordinates of the safe spots , seperated by a single space. Both coordinates are integer values. There are no leading or trailing spaces or blank lines. 0<k≤2200

Output

For each case print a single integer by itself on a line, with no leading or trailing spaces. Do not print blank lines.

Example

Input:
2
5
0 0
1 1
2 2
4 8
2 75
3
0 0
1 2
3 4


Output:
2
1

Added by:	Abhilash I
Date:	2007-02-22
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Code Craft 2007

SPOJ Problem Set (classical)

1329. Matrix

Problem code: KPMATRIX

The company you work in has got a secret job to do. Just a few persons know what it is all about. To keep a secret every programmer works on a small part of the project.

Your job is as follows. You are given a matrix of integer numbers with N rows and M columns. Also two integer numbers A and B are given. Your task is to find a number of submatrices of a given matrix with the sum of elements between A and B inclusively.

Input

The first line contains two integer numbers N and M (1 ≤ N, M ≤ 250). After that matrix description follows. N lines with M numbers each. The last line contains two integer numbers A and B (-10^9 ≤ A ≤ B ≤ 10^9). All numbers separated with spaces. It's guaranteed that for every submatrix the absolute value of sum of it's elements will not exceed 10^9.

Output

Write to the output the number of submatrices of a given matrix with sum of their elements between A and B inclusively.

Example

Input:
3 3
1 0 0
0 1 0
0 0 1
1 3

Output:
26

Added by:	Pavel Kuznetsov
Date:	2007-02-23
Time limit:	1s-10s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS
Resource:	IT Festival Arkhangelsk 2006

SPOJ Problem Set (classical)

1335. Maze

Problem code: KPMAZE

The King of Byteland likes Greek mythology very much. The most impressive myth for him is the one about Minotaur. A creature which was imprisoned in a maze-like construction. Now The King wants to have similar maze. He ordered to his architect to build such construction.

The architect decided that maze will have rectangular form. Its floor will be made from large square plates. Also there will be many walls, each of which will separate two common floor plates. From the bird's eye whole construction will look like a grid with some cells separated by walls. The maze should be very tricky, that's why he calls the maze correct if and only if for every two plates there is exactly one path between them. Here path is a sequence of moves between plates that share a common side and are not separated by wall. Each plate can only appear once in a path.

Sooner or later, the architect started his work. After a couple of months he created a rectangular area with H rows and W columns. Also he has built K walls. Sounds perfect but he was seized with a lingering doubt about correctness of his maze.

That's why he asks you to help him. He wants to know how many different correct mazes can be built based on his current maze i.e. you can only add new walls but not to break any of the old ones.

For example (see figure 1.) the maze size is 2x2 and there are no walls. All four ways to complete this maze are shown on the right of the figure (new walls are dashed).

Figure 2. illustrates maze of size 3x3 with 3 walls. There are exactly 4 ways to complete it.

Figure 3. shows the maze that cannot be completed, because there is no path from lower right plate to upper left one.

Input

The first line contains two integer numbers W and H (1 ≤ W, H ≤ 5). Second line contains one integer number K (K ≥ 0). Next K lines contain description of walls. Each wall is determined by two plates it separates. Thus, each line contains four integer numbers: R_1, C_1, R_2 and C_2, here R_1 and C_1 - row and column coordinates of the first plate. Similar, R_2 и C_2 - are coordinates of the second plate (1 ≤ R_1, R_2 ≤ H, 1 ≤ C_1, C_2 ≤ W). Rows are numbered from up to bottom, colums - left to right started from 1. It is guaranteed that all walls are correct and there are no duplicates. Walls that form perimeter of the maze will not be specified.

Output

Output the number of different correct mazes that can be built based on the given one. There should be no leading zeroes.

Example

Input:
2 2
0

Output:
4

Input:
3 3
3
3 1 3 2
2 2 2 3
2 3 3 3

Output:
4

Input:
3 3
5
3 1 3 2
2 2 2 3
2 3 3 3
2 2 2 1
1 2 2 2

Output:
0

Added by:	Pavel Kuznetsov
Date:	2007-02-24
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	IT Festival Arkhangelsk 2006

SPOJ Problem Set (classical)

1391. Summing to a Square Prime

Problem code: CZ_PROB1

S_P2 = {p | p = x₁² + x₂² for some x₁, x₂ belonging to Z} is the set of all primes that can be represented as the sum of any two squares. The function S_P2(n) gives the n^th prime number from the set S_P2. Now, given two integers n (0P2(n), k) where p(a, b) gives the number of unordered ways to sum to the given total ‘a’ with ‘b’ as its largest part. For example: p(5, 2) = 3 {2+2+1, 2+1+1+1, and 1+1+1+1+1}. Here 5 is the total with 2 as the largest part.

Input

The first line gives the number of test cases T followed by T lines of integer pairs, n and k.
Scope:
0 < T < 501
0 < n < 501
1 < S_P2(n) < 7994
0 < k < 4

Output

The p(S_P2(n), k) for each n and k. Append a newline character to every test cases’ answer.

Example

Input:
3
2 2
3 2
5 3

Output:
3
7
85

Added by:	Rahul
Date:	2007-03-10
Time limit:	2s
Source limit:	3000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Sam Collins

SPOJ Problem Set (classical)

1418. The Cats and the Mouse

Problem code: CATM

In a rectangular field of size n by m squares there is a mouse and two cats. The mouse is the first to make a move, then each of the cats makes a move, then again its the mouse's turn, and so on. In each move both the mouse and the cats can move exactly one square vertically or horizontally. If the mouse is standing at the edge of the field then in its next move it can jump off the field and is saved from the cats. If in the next move one of the cats moves to the field with the mouse then there is no escape for the mouse ... =(

You are to write a program which, knowing the initial positions of mouse and the two cats, will find out if there is any way for the mouse to escape from the cats, assuming of course that each cat will do its best to catch the mouse.

Input

In the first line of input two integers n and m are given, not exceeding 100, where n is the number of rows, and m - the number of columns. The second line contains a number k [k <= 10], which defines the number of test cases for the given field. In the next k lines the initial positions of the mouse and the cats are given. The position in the field is given by two numbers: the first is the number of the row, the second is the number of the column. The first two integers are the coordinates of the mouse, the next four integers are the coordinates of the cats.

Output

You must output k lines with answers for each test case. The answer is YES, if the mouse can escape or NO otherwise.

Example

Input:
5 3
3
2 2 1 1 3 3
2 3 1 3 5 2
3 2 1 2 4 3

Output:
NO
YES
YES

Author: Filimonenkov D.O.

Added by:	Roman Sol
Date:	2006-05-04
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	ZCon 2007

SPOJ Problem Set (classical)

1419. A Game with Numbers

Problem code: NGM

Nikifor and Trofim play the following game: they write some integer smaller then 2000000000 and take turns one after another. Nikifor is the first to make a move. The turn is made by the following rule: from the written integer any non-zero digit is subtracted, and the new integer replaces the old one on the desk. For example for integer 40534, the next move can be: 40530, 40531 or 40529. The winner is the player who writes zero on the desk.

Write a program to decide who will win if both players do their best.

Input

The input contains the integer from which the game is started.

Output

In the first line you must write 1 if Nikifor wins and 2 otherwise. If Nikifor wins then in the second line you must output the move in the first turn which guarantees victory for him. If there are many such moves then output any of them.

Example

Input:
14

Output:
1
4

Author: Filimonenkov D.O.

Added by:	Roman Sol
Date:	2006-05-05
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	ZCon 2007

SPOJ Problem Set (classical)

1420. Geometry and a Square

Problem code: GEOM

Is there anyone who doesn't love geometry?! Just imagine: on the plane you are given a square ABCD, with vertices given in the clockwise direction. Also given is a point P which is different from all of A, B, C or D. Have you imagined it? Interested? Ok, let's continue!

Through vertex A a line a is drawn that is perpendicular to line BP, through vertex B a line b is drawn that is perpendicular to line CP, through vertex C a line c is drawn that is perpendicular to line DP, through vertex D a line d is drawn that is perpendicular to line AP. Do the lines a, b, c and d cross each other in one point? Ok, it depends on what the square is and what point P is given. Write the program that discovers if these lines cross in one point, and if so, finds the coordinates of this point.

Input

In the first line you are given the integer coordinates of the point in which diagonals of the square intersect. In the second line you are given one integer - the length of the side of the square. In the third line you are given the integer coordinates of point P. The integers do not exceed 100, in terms of absolute value.

Output

For each test case you must output YES if the sought point exsists, and NO otherwise. If you answer YES then in the second line you must output the coordinates of the intersection point. Coordinates must be rounded to one digit after the point.

Example

Input:
10 10
20
5 12

Output:
YES
8.0 5.0

Author: Filimonenkov D.O.

Added by:	Roman Sol
Date:	2006-05-05
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	ZCon 2007

SPOJ Problem Set (classical)

1421. Goods

Problem code: FIRM

There are n dealers in the market. Each of them has some unique goods (nobody else has the same goods). Besides, each of them wants to obtain some other goods, which exist in the market. This is rather strange, but for each kind of goods on the market there exists exactly one dealer who wants to obtain it.

To prevent fraud, only exchanges in pairs are allowed in this market. Moreover, each dealer is allowed to make at most one exchange a day. But the total number of transactions isn’t limited. A transaction means that all the goods of one dealer are exchanged for all the goods of the other participating dealer (partial transactions are not allowed).

You are to write a program which outputs the minimum number of days needed for each dealer to get the goods that he wants. Also output one of the possible variants of exchanges leading to this goal.

Input

The first line contains an integer n [n <= 5000]. In the second line exactly n numbers of goods are given, which the dealers require. If integer j appears as the i-th at input, then this means that goods required by dealer i are initially owned by dealer j.

Output

You must output the minimum number of days m which are needed to complete the transactions. In the next m lines you must output the way these transactions should be managed by the dealers. One line corresponds to one day. At the beginning of each line you must output the number of transactions on this day. After that output the pairs of dealers who exchange their goods on this day. Dealers in pairs are separated by '-' symbol. If there are many ways to perform the exchanges then output any of them.

Example

Input:
7
2 1 3 5 6 7 4

Output:
2
3 1-2 4-5 7-6
1 5-7

Author: Filimonenkov D.O.

Added by:	Roman Sol
Date:	2006-05-05
Time limit:	1s-10s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	ZCon 2007

SPOJ Problem Set (classical)

1431. Projections Of A Polygon

Problem code: KPPOLY

You are given a convex polygon on Cartesian coordinate system. It has projections on X and Y-axis. You can arbitrary rotate this polygon. What minimum and maximum sum of projections can you achieve?

Input

First line contains one integer number N (3 ≤ N ≤ 100) - number of polygon's vertices. Following N lines contain vertex coordinates X_i and Y_i. All numbers are integers. Vertices are given in clockwise or anticlockwise direction. No two vertices coincide. No three consecutive vertices lie on the same line. All coordinates do not exceed 10000 by absolute value.

Output

Write minimum and maximum value of sum of the polygon's projections. Separate them by a space. Your answer should not differ with the correct one more than 10^-6.

Example

Input:
4
0 0
0 1
1 1
1 0

Output:
2 2.828427124

Added by:	Pavel Kuznetsov
Date:	2007-03-25
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	Vologda 2007

SPOJ Problem Set (classical)

1433. The Sum

Problem code: KPSUM

One of your friends wrote numbers 1, 2, 3, ..., N on the sheet of paper. After that he placed signs + and - between every pair of adjacent digits alternately. Now he wants to find the value of the expression he has made. Help him.

For example, if N=12 then +1 -2 +3 -4 +5 -6 +7 -8 +9 -1+0 -1+1 -1+2 = 5

Input

Each line contains one integer number N (1≤ N ≤ 10¹⁵). Last line contains 0 and shouldn't be processed. Number of lines in the input does not exceed 40.

Output

For every line in the input write the answer on a separate line.

Example

Input:
12
0

Output:
5

Added by:	Pavel Kuznetsov
Date:	2007-03-26
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Vologda 2007

SPOJ Problem Set (classical)

1434. Equation

Problem code: KPEQU

You are given integer positive number N. Find the number of solutions in positive integer numbers of the following equation:

1/N! = 1/X + 1/Y

Input

Each line of input file contains one integer number N (1 ≤ N ≤ 10⁴). The last line contains 0 and shouldn't be processed. Number of lines in the input does not exceed 30.

Output

For every line in the input write the answer on a separate line.

Example

Input:
1
2
0

Output:
1
3

Added by:	Pavel Kuznetsov
Date:	2007-03-27
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Vologda 2007

SPOJ Problem Set (classical)

1435. Vertex Cover

Problem code: PT07X

You are given an unweighted, undirected tree. Write a program to find a vertex set of minimum size in this tree such that each edge has as least one of its end-points in that set.

Input

The first line of the input file contains one integer N --- number of nodes in the tree (0 < N <= 100000). Next N-1 lines contain N-1 edges of that tree --- Each line contains a pair (u, v) means there is an edge between node u and node v (1 <= u,v <= N).

Output

Print number of nodes in the satisfied vertex set on one line.

Example 1

Input:
3
1 2
1 3

Output:
1

Explanation:
The set can be {1}

Example 2

Input:
3
1 2
2 3

Output:
1

Explanation:
The set can be {2}

Added by:	Thanh-Vy Hua
Date:	2007-03-28
Time limit:	1.200s-8s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Co-author Amber

SPOJ Problem Set (classical)

1436. Is it a tree

Problem code: PT07Y

You are given an unweighted, undirected graph. Write a program to check if it's a tree topology.

Input

The first line of the input file contains two integers N and M --- number of nodes and number of edges in the graph (0 < N <= 10000, 0 <= M <= 20000). Next M lines contain M edges of that graph --- Each line contains a pair (u, v) means there is an edge between node u and node v (1 <= u,v <= N).

Output

Print YES if the given graph is a tree, otherwise print NO.

Example

Input:
3 2
1 2
2 3

Output:
YES

Added by:	Thanh-Vy Hua
Date:	2007-03-28
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS
Resource:	Co-author Amber

SPOJ Problem Set (main)

1437. Longest path in a tree

Problem code: PT07Z

You are given an unweighted, undirected tree. Write a program to output the length of the longest path (from one node to another) in that tree. The length of a path in this case is number of edges we traverse from source to destination.

Input

The first line of the input file contains one integer N --- number of nodes in the tree (0 < N <= 10000). Next N-1 lines contain N-1 edges of that tree --- Each line contains a pair (u, v) means there is an edge between node u and node v (1 <= u,v <= N).

Output

Print the length of the longest path on one line.

Example

Input:
3
1 2
2 3

Output:
2

Added by:	Thanh-Vy Hua
Date:	2007-03-28
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	C C++ 4.0.0-8
Resource:	Co-author Amber

SPOJ Problem Set (classical)

1440. Use of Function Arctan

Problem code: ARCTAN

It's easy to know that arctan(1/2)+arctan(1/3)=arctan(1).The problem is,to some fixed number A,you have to write a program to calculate the minimum sum B+C.A,B and C are all positive integers and satisfy the equation below:

arctan(1/A)=arctan(1/B)+arctan(1/C)

Input

The first line contains a integer number T(about 1000).T lines follow,each contains a single integer A, 1<=A<=60000.

Output

T lines,each contains a single integer which denotes to the minimum sum B+C.

Example

Sample input:
1
1

Sample output:
5

Some new test data has been added on Feb.15, 2009, 36 users lose their Accepted.

Added by:	[Trichromatic] XilinX
Date:	2007-03-31
Time limit:	10s
Source limit:	256B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2001,Day 1; translated by Blue Mary

SPOJ Problem Set (classical)

1441. The Clever Typist

Problem code: CLEVER

Blue Mary is a typist of some secret department.Now she have to type in many passwords in an hour,each of which has a fixed length: 6.Of course,the less times she presses the keyboard,the happier she is.

Unfortunately,the keyboard to type in the password is extraordinary designed to keep secrets.The keyboard has 6 particular keys instead of 10 number keys.To explain the uses of these keys,let's define the 6 position on the screen 1,2,3,4,5,6 from left to right.The keys' uses are shown below:

Swap0: swap the digit in the cursor position and the digit in position 1.The cursor doesn't move.If the cursor is now in position 1,the digits on the screen won't be changed.
Swap1: swap the digit in the cursor position and the digit in position 6.The cursor doesn't move.If the cursor is now in position 6,the digits on the screen won't be changed.
Up: increase the digit in the cursor position by 1.If the digit in the cursor position is 9,no change will happen.
Down: decrease the digit in the cursor position by 1.If the digit in the cursor position is 0,no change will happen.
Left: move the cursor one position left.If the cursor is in position 1,no change will happen.
Right: move the cursor one position right.If the cursor is in position 6,no change will happen.

At start,6 random digits will be given on the screen,and the cursor will in position 1.After some smart presses,she can type in the correct password,at that time the cursor position is unimportant.

Here is an example("()"denotes to the cursor):

key pressed       screen
                  (1)23456
Swap1             (6)23451
Right             6(2)3451
Swap0             2(6)3451
Down              2(5)3451
Right             25(3)451
Up                25(4)451
Right             254(4)51
Down              254(3)51
Right             2543(5)1
Up                2543(6)1
Swap0             6543(2)1

Now Mary wants to know the minimal number of keys she has to press.Can you help her?

Input

The first line contains a single integer t(about 1000).t lines follow,each contains two 6-digit string,which show the digits on the screen at start and the password Mary is to type in,separated by a single space.

Output

t lines,each contains a single integer - the answer.

Example

Sample input:
1
123456 654321

Sample output:
11

Some new test data has been added on Feb 15,2009. 26 users lose their Accepted.

Added by:	[Trichromatic] XilinX
Date:	2007-03-31
Time limit:	7s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2001,Day 1; translated by Blue Mary

SPOJ Problem Set (classical)

1442. Strange Food Chain

Problem code: CHAIN

There are 3 kinds of animals A,B and C. A can eat B,B can eat C,C can eat A. It's interesting,isn't it?

Now we have n animals,numbered from 1 to n. Each of them is one of the 3 kinds of animals:A,B,C.

Today Mary tells us k pieces of information about these n animals. Each piece has one of the two forms below:

1 x y: It tells us the kind of x and y are the same.
2 x y: It tells us x can eat y.

Some of these k pieces are true,some are false. The piece is false if it satisfies one of the 3 conditions below, otherwise it's true.

X or Y in this piece is larger than n.
This piece tells us X can eat X.
This piece conflicts to some true piece before.

Input

The first line contains a single integer t.t blocks follow.

To every block,the first line contains two integers n(1<=n<=50000) and k (1<=k<=100000). k lines follow,each contains 3 positive integers D(1<=D<=2),X,Y,separated by single spaces.

Output

t lines,each contains a single integer - the number of false pieces in the corresponding block.

Example

Sample input: 1 100 7 1 101 1 2 1 2 2 2 3 2 3 3 1 1 3 2 3 1 1 5 5 Sample output: 3 Hint:

The false pieces are the 1st,the 4th and the 5th ones.

Warning: large Input/Output data, be careful with certain languages

Added by:	[Trichromatic] XilinX
Date:	2007-03-31
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2001,Day 1; translated by Blue Mary

SPOJ Problem Set (classical)

1444. DEL Command II

Problem code: DELCOMM2

It is required to find out what's the maximum number of files that can be deleted from MS-DOS directory executing the DEL command of MS-DOS operation system only once. There are no nested subdirectories.

A note

DEL command has the following format: DEL wildcard

The actual wildcard as well as a full file name can be made up of a name containing 1 up to 8 case-sensitive characters. In a wildcard the characters '?' and '*' can be used. A question mark substitutes exactly one character of the full file name, an asterisk any sequence of characters even empty one.

MS-DOS system can permit maybe other wildcards but they can not be used in this task. File names consist only of Latin letters and digits.

Input

The first line of the input is an integer M, then a blank line followed by M datasets. There is a blank line between datasets.

Input data for each dataset contains a list of full file names without any extra empty lines and spaces. Each name is written in a separate line of input data file and ended with a control sign: '+' for delete or '-' for keep. Full file names are not repeated. The list comprises at least one file, and at least one file is marked to be deleted. There are no more than 250 files.

Output

For each dataset, write to the first line of output the maximum number of files one DEL command can delete.

Example

Input:

2

BP +
BPC +
TURBO -

EXCHANGE +
EXT +
HARDWARE +
MOUSE –
NETWORK –

Output:

2
2

Hint:

For the two tests above,the corresponding DEL commands are DEL BP* and DEL EX*.

Link

You can try problem DELCOMM first. It's far easier than this problem.

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	35s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 1997,Day 1

SPOJ Problem Set (classical)

1447. A Game of Toy Bricks

Problem code: BRCKGAME

Blue Mary invents a game with toy bricks. The player has N cuboids numbered from 1 to N.

The rule of the game is discribed below:

Choose some cuboids among the N cuboids, and divide them into M(1 <= M <= N) piles,named them Pile₁,Pile₂ ... Pile_M. There are at least 1 cuboid in each pile. To make the game easier, for any cuboid in Pile_K,its id should greater than any one in Pile_K+1 (1 <= K < M).
For each pile of cuboids,the player will put them as a tower, and he should follow the two rules below:
The up surface of each cuboid is touched and only touched another down surface. Luckily,to make the pile looking like a tower,the up surface of the lower cuboid should cover the down surface of the higher cuboid,i.e. the length of the lower up surface is not less than that of the higher down surface, and also to the width.
In each pile,the lower cuboid has a less id than the higher cuboid.

Your task is to find a method,to make the sum of the height of each pile maximum.

Input

The very first line of the input contain the number t,then t cases follow.

For each case,The first line contain two integer number N and M. N(N<=100) is the total number of the cuboids, M(M<=N) is the number of the piles, separated by a single space.

Then N line follow, which are the description of the cuboids 1..N. Each line contains three integer numbers(<=1000)- the length, width and height of that cuboid,separated by spaces.

Output

For each case, the output contains only one line with a single integer number - the maximum sum.

Example

Sample Input:
1
4 2
10 5 5
8 7 7
2 2 2
6 6 6

Sample Output:
24

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	3s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 1997,Day 2; translated by Blue Mary

SPOJ Problem Set (classical)

1448. 3D Cover

Problem code: COVER2

In the 3D Cartesian coordinate system, there are n cubes.These cubes are all axis-paralleled. What's the volume of the union of these cubes?

Input

There is a single integer m in the very first line of the input, the number of test cases. m blocks follow.

For each test, the first line contains a single integer n(1<=n<=100), the number of cubes. n lines follow, each contains four integers x,y,z,r(-1000<=x,y,z<=1000,1<=r<=200), separated by spaces. x,y,z are the X,Y,Z coordinates of the center of the cube, and r is the distance between the center and any surface of the cube.

Output

m lines,each contains a single integer - the answer.

Example

Sample Input:
1
3
0 0 0 3
1 -1 0 1
19 3 5 6
Sample Output:
1944

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	2s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 1997,Day 2; description by Blue Mary

SPOJ Problem Set (classical)

1451. 01 Sequence

Problem code: SEQ1

The input consists of exactly 5 test cases in the following format:

Input

N A0 B0 L0 A1 B1 L1 [3<=N<=1000,1<=A0<=B0<=L0<=N,1<=A1<=B1<=L1<=N]

Output

Exactly 5 lines,each contains:

a) A sequence (We name it S) consisting only characters '0' and '1' and no extra whitespaces, which satisfy the following conditions:

The number of '0' in any consecutive subsequence of S whose length is L0 is not more than B0 and not less than A0.
The number of '1' in any consecutive subsequence of S whose length is L1 is not more than B1 and not less than A1.

b)A single number -1,if the sequence which satisfies the conditions above doesn't exist.

Example

Input:
6 1 2 3 1 1 2
[and 4 test cases more]

Output:
010101
[and 4 test cases more]

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 1999,Day 1; translated by Blue Mary

SPOJ Problem Set (classical)

1452. Birthday Cake

Problem code: CAKE

Adolf wants to send a cake to Blue Mary to celebrate her birthday. The cake looks like a tower which has M floors, each floor is a cylinder. The i-th cylinder counted from downside to upside has a integer height h_i and a integer radius r_i. These numbers fulfill the following two conditions:

h₁ > h₂ > h₃ > ... > h_M
r₁ > r₂ > r₃ > ... > r_M

Adolf is interested in minimising the area of the surface of the cake, except for the underside of the lowest cylinder. He needs your help because of his poor math knowledge.

Input

The very first line contains a integer number T. T test cases follow.

For each test case, the first line contains a single integer number N (N<=10000), the second line contains a single integer number M (M<=10). The cake must be made of M cylinders and its volume must be N*Pi.

Output

For each test case, a single line containing a single integer S must be written to output. The required minimum area must be S*Pi.

Example

Sample Input:
1
100
2

Sample Output:
68

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 1999,Day 1; translated by Blue Mary

SPOJ Problem Set (classical)

1453. Optimal Connected Subset

Problem code: OPTSUB

A point P(x,y) is called an integer point if and only if both x and y are integers.
W is the set which contains all the integer points on the plane.
Two integer point P(x,y) and Q(x',y') are called adjacent if and only if |x-x'|+|y-y'|=1.
S is a set of integer points if and only if S is a limited subset of W.
If S is a set of integer points, R and T belong to S,and there exist a limited integer point sequence Q₀(=R),Q₁,Q₂,...,Q_k,Q_k+1(=T) which satisfies that
- Q_i!=Q_j iff i!=j
- Q_i and Q_i+1 are adjacent, for each 0<=i<=k.
- Q_i belongs to S, for each 0<=i<=k+1.
we call R and T are connected and the sequence Q_i(0<=i<=k) is a path that connect R and T.
If S is a set of integer points, X and Y are some integer points that belong to S, there exists one and only one path connected X and Y, then S is called an optimal set.

Given an optimal set V, your task is to find an optimal set B, satisfying that B is a subset of V and the sum of the weights of each integer point is maximum.

Input

The very first line of the input contains a single integer T, the number of test cases. T blocks follow.

For each test case, the first line contains a single integer N=|V|(N<=1000). N lines follow, each contains 3 integers, the X-coordinate, the Y-coordinate and the weight(the absolute value of the weight<=100) of the ith integer point, separated by single spaces.

Output

T lines,each contains a single integer - the maximum sum of weights.

Example

Input:
1
5
0 0 -2
0 1 1
1 0 1
0 -1 1
-1 0 1

Output:
2

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 1999,Day 2; translated by Blue Mary

SPOJ Problem Set (classical)

1454. Memory Distribution

Problem code: MEMDIS

EMS memory (called memory for short) is some important resource of a computer. When a program is running, the computer must distribute the memory for it.

The classical memory distribution process is like the following:

The basic unit of the memory is called a cell, each cell is assigned to a fixed integer number called its address. The address starts from number 0. If two cell's address numbers are two consecutive integer numbers, the two cells are called (logically) consecutive. We name the s consecutive cells starting from address i a piece whose length is s and first address is i.
Many programs need memory during their running. For each program, we need a application time X, a number of cells needed M and a running time P to describe it. When the program is running(during it starts running (time T) to T+P, including the left end and excluding the right end),The M cells cannot be used by other programs.
Suppose a program apply M cells at time X and its running time is P,then
- (A) If there is a piece in the memory at time X, each cell of which is not being used, and whose length is M, the computer will distribute these M cells to this program. If there are more pieces, the computer will choose the one whose first address is minimum.
- (B) If such piece does not exist at time X, the program will be put into a queue.If after some time, there exist a piece whose length is M and the corresponding program is at the head of the queue, the computer will pop this program and distribute memory for it like (A) immediately. During the process of memory distribution, the programs which are not at the head of the queue cannot start to run before the one at the head of the queue.

Input

Ten test cases (given one after another, you have to process all!).For each test case:

The first line is a number N, which shows the number of memory cells. There addresses are 0..n-1. Less than 10000 lines follow, each contains 3 integers X, M(M<=N), P describing the programs. A line containing three zeroes denotes the end of a test case. The programs have been sorted by there application time X.

All numbers in the input and output file will be less than 10⁹.

Output

For each test case output two lines. The first line contains a single integer, which shows the time when all the programs have been run and stops normally. The second line contains a single integer, which is the number of programs which has been put into the queue.

Example

Input:
10
1 3 10
2 4 3
3 4 4
4 1 4
5 3 4
0 0 0
[and 9 test cases more]

Output:
12
2
[and 9 test cases more]

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	17s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 1999,Day 2; translated by Blue Mary

SPOJ Problem Set (classical)

1455. Program Analyser

Problem code: ANALYSER

Input

A Program which has the following format:

<Program>::=<sentence><line break>{<sentence><line break>}
<setence>::=<level><space><body>
<body>::=<addition> | <output> | <goto> | <condition> | <end>
<addition>::=<variable>+<integer>
<output>::=<variable>?
<goto>::=GO<space><level>
<condition>::=IF<space><variable>=<integer><space><goto>
<end>::=END
<variable>::=<character>
<level>::=<integer>
<integer>::=<digit>{<digit>}
<character>::=A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z
<digit>::= 0|1|2|3|4|5|6|7|8|9
<line break>::=(ASCII 10)
<space>::=(ASCII 32)

The program runs following the following rules:

Program starts from the sentence whose level is minimum, and executed by the level from low to high except that the sentence is<goto>or<condition>.
All variables are initialized to 0.
<Addition>means<variable>+=<integer>in C++.
<output>means write the value of<variable>to the output file(we aren't interesting about the real output file.)
<condition>means if and only if the value of the <variable> equals to <integer>, <goto> will be executed, otherwise the next sentence executed is as usual.
After<goto>, the next sentence executed is the sentence with level which equals to the level in<goto>.
Program terminates by itself when <end> is executed.
The numbers during the program is running will fit in a signed 32-bit integer.
The number of sentences in the program is not more than 100.
The length of each line in the input file is not more than 20.
The input is correct.
The sentence with the maximum level is always <end>.
Any level is not more than 3000.

Input terminate by EOF.

Output

Output the number of sentences executed.If the program can not terminate by itself,output -1.

Example

Input:
10 A+1
20 IF A=5 GO 60
60 END
30 A+2
40 A?
50 GO 20

Output:
11

Hint:
10->20->30->40->50->20->30->40->50->20->60

Note

You may try problem ANALYS_T first. It's the same problem with this one and its time limit is not so strict.

Log

The time limit of this problem has been changed from 0.4/0.5 second to 1 second per test on Jun.5, 2008. All the solutions have been rejudged.

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2000,Day 1; translated by Blue Mary

SPOJ Problem Set (classical)

1457. Help Blue Mary Please! (Act I)

Problem code: BLUEEQ

This morning Blue Mary wrote some equations on a piece of paper and left it on her desk. After solving some problems in SPOJ, she found that her classmate H.L. replaced all characters on the paper with some other ones. H.L. told her he replaced the same characters with the same ones, and different characters with different ones because of his goodness. Now Mary needs your help to get the original equations back.

In Mary's equations, only 13 characters appear:0,1,2,3,4,5,6,7,8,9,+,*,=. There is one and only one "=" in each equation. In H.L.'s equations,only 13 Latin letters appear: a,b,c,d,e,f,g,h,i,j,k,l,m. All the equations are correct in decimal notation.

For example. If Mary wrote down 2+29=31, H.L. replaced 2 with i, + with l, 9 with k, = with e, 3 with m and 1 with a, we got ilikema .

Input

The first line contains a single integer t.t blocks follow.

To every block,the first line contains a single integer n(1<=n<=1000). n lines follow,each contains a string whose length is more than 4 and less than 12.The string contains only a-m and doesn't contain any whitespaces.

At least 90% of test cases satisfy that n<=5.

At least 80% of test cases satisfy that n<=2.

In at least 70% of test cases, there are at most 5 different characters in all the equations.

Output

If there doesn't exist n equations that can be translated to H.L.'s equations,print a line contains the word noway .Otherwise you should output all the corresponding relations that can be fixed in lexicographic order,see the example.

Example

Input
1
2
abcdec
cdefe

Output
a6
b*
d=
f+

hint

The two strings can be translated to the following equations possibly:

6*2=12 2=1+1
6*4=24 4=2+2
6*8=48 8=4+4

So the corresponding relations above can be fixed,others can not.

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	17s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2000,Day 2; translated by Blue Mary

SPOJ Problem Set (classical)

1458. Help Blue Mary Please! (Act II)

Problem code: BLUEEQ2

Today Mary's math homework is to solve an equation.

She knows all ki and pi, and 1<=xi<=M. All xi must be integers. She must work out the number of different solutions of this equation this day.Can you give her a hand?

Input

There is a single integer T in the very first line of the input denoted the number of tests.T blocks follow.

For each test case:

The first line contains a single integer n(n<=6).The second line contains a single integer m(m<=150).n lines follow,each contains two space-separated integers ki and pi, i=1,2,...,n. All pi are positive.

Output

For each test case output a single line ,which contains a single integer - the answer.You may assume this number is less than 2^31.

Example

Input:
1
3
150
1 2
-1 2
1 2

Output:
178

Warning: The time limit is very strict for this problem.

Blue Mary's Note: test data were modified on Dec.4, 2007. All the solutions have been rejudged.

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	11s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2001,Day 2; translated by Blue Mary

SPOJ Problem Set (classical)

1459. The Secret of an Aerolite

Problem code: AEROLITE

A huge aerolite had fallen in Antarctica!!!Many disasters happened and lots of people lost their lives, homes or even everything.Blue Mary, the well-known scientist, is to work out the secret of this aerolite for further study.

Blue Mary has found out that their are some numbers on this aerolite, 5 per line:

1 1 1 1 6
0 0 6 3 57
8 0 11 3 2845

With her genius, Blue Mary knows that the 5th number is the key to solve the problem, but in some lines the 5th numbers were destoryed and we cannot know what they are instantly.

After some days, she finds out the way to calculate the 5th number finally, which is:

A Regular Expression(RE) is a string which only contains characters '{','[','(',')',']','}' and satisfies the rules below.
An empty string is an RE.
If there's no character '[',']','{','}' in RE A, then (A) is an RE.
If there's no character '{','}' in RE A, then [A] is an RE.
If A is an RE, {A} is an RE.
If both A and B are REs, AB is an RE.

For example "()(())[]", "{()[()]}", "{{[[(())]]}}"(all without quotes) are REs and "()([])()","[()" are not REs.

The deep of an RE A, D(A), is defined as below:

If A is an empty string,D(A)=0;
If A can be written as BC, D(A)=max(D(B),D(C));
If A can be written as (B) or [B] or {B}, D(A)=D(B)+1.

Such as D("(){()}[]")=2.

Suppose the first 4 numbers in current line are L1,L2,L3 and D, then the 5th number in current line is the number of REs modudo 11380.Each of the REs must have a depth of D and is made of L1 {}, L2 [] and L3 ().

Now Mary needs your help to work out the 5th number.

Input

Input contains exactly 10 test cases.Each test case contains one line, which contains 4 numbers L1,L2,L3,D(0<=L1,L2,L3<=10, 0<=D<=30), separated by single spaces.

Output

Ten lines, each contains a single integer denoted the 5th number.

Example

Input:
1 1 1 1
0 0 6 3
1 1 1 2
[and 7 test cases more]

Output:
6
57
8
[and 7 test cases more]

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	7s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2001,Day 2; translated by Blue Mary

SPOJ Problem Set (classical)

1460. A Simple Calculator in the Galaxy

Problem code: GALAXY

Background

So if you want to survive the Earth's demise and see the galaxy, make sure you are wearing something more substantial than pajamas and a ratty bathrobe, watch the skies for flying saucers, start worrying when all the dolphins on the planet vanish, and keep your eyes peeled for an electronic gizmo with the words "Don't Panic" printed in large friendly letters on the cover.

--The Hitchhiker's Guide to the Galaxy

Problem

Addition,subtration and multiplication is necessary wherever you are in the galaxy.You are to write a program to perform these operations, and you can see 6*7=42 or 67-25=42 or 31+11=42, maybe one of them is the problem of Life, the Universe and Everything.

Please note that the solution may only be submitted in Brainf**k, Whitespace and Intercal, other languages like C/C++/Pascal/Java are not allowed! If you want to use other languages to solve this problem, you may try this one.

Input

Multiple test cases, the number of them T is given in the very first line, T<=99.

Each test case contains one line which has the following form:

num oper num

where num is an integer number between 1 and 99, and oper is '+' or '-' or '*' (without quotes).

There's no extra whitespace and leading zero in the input.

Output

For each test case you should output one line which contains the answer without any leading zeros.You may assume this number is always a positive one.

Example

Input:
3
6*7
67-25
31+11

Output:
42
42
42

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	17s
Source limit:	17000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	BF ICK WSPC
Resource:	Folklore, description and test data by Blue Mary

SPOJ Problem Set (classical)

1461. Greedy Hydra

Problem code: DRAGON

Hydra is some very greedy animal. A hydra has 9 heads when he is born, and many more new heads will come out when he grows up. Of course, some old heads will break off because of caducidy.

One day, a hydra with M heads finds a tree with N fruits on it. He is very delighted and wants to eat this tree instantly. Since he has M heads, he must divide these N fruit into M groups, each group contains at least 1 fruit, and each head will eat a group of fruits.

The biggest head among the M heads is named "Boss", it must eat neither more nor less than K fruits, and, in the nature of things, the biggest fruit included. These fruits are connected by N-1 branches, and there exists a path made up with branches between each pair of fruit.

If two fruit connected by a single branch is put in different groups, the corresponding two heads will break the branch and eat the two fruits, otherwise the corresponding head will eat the two fruits without breaking the branch. Eating branches is not very comfortable of course, so every branch has a weight of illness, and the weight of illness of this hydra is the sum of the weights of illness of all brances he has eaten.

Your task is to help the hydra to minimize his weight of illness.

The picture below is an example.

N=8,M=2,K=4.The bigger head eats 4 fruits(full points), the smaller head eats 4 fruits(empty points). The branch signed by a thin segment is eaten by the hydra.

Input

Ten test cases(Given one after another, you have to process all!). For each test case the first line contains 3 integers N(1<=N<=300),M(2<=M<=N),K(1<=K<=N), separated by single spaces. The N fruits are numbered 1..N, and the biggest fruit is always numbered 1. N-1 lines follow, each contains 3 integers i,j,k separated by spaces denoted that there is a branch between fruit i(1<=i<=N) and fruit j(1<=j<=N) and the weight of illness of this branch is k(0<=k<=100000).

Output

Ten lines, each contains a single integer - the minimum weight of illness of the hydra. If we can't divide the fruit into M groups, output "-1"(without quotes).

Example

Input:
8 2 4
1 2 20
1 3 4 
1 4 13
2 5 10
2 6 12
3 7 15
3 8 5
[and 9 test cases more]

Output:
4
[and 9 test cases more]

Link

After solving this problem you can try the problem DRAGON2.

Blue Mary's Note: test data has been modified on Dec.12, 2007. All the solutions have been rejudged.

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	9s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2002,Day 1; translated by lcosvse

SPOJ Problem Set (classical)

1462. Barbarians

Problem code: BARB

There are N Barbarians living on an unknown island. On the island there are M caves, we can number them 1, 2, ..., M clockwise. When we find the island, the barbarians are living in N distinct caves numbered C1,C2,...,CN.Every year each barbarian walks out of his cave and goes along the road,passes Pi caves and then go into that cave.Every Barbarian has a living time: Li years, after Li years the ith barbarian died.

We are surprised to find out that no two barbarians live in one cave in the same year so no conflicts have happened.We are interesting about the minimum number of caves on the island.

Please note that this problem has a somewhat strict source limit and time limit.

Input

The very first line contains a single integer T,the number of test cases.T blocks follow.

For each test case, the first line contains a single integer N(N<=15).N lines follow,each contains 3 integers Ci(1<=Ci<=100),Pi(1<=Pi<=100),Li (1<=Li<=1,000,000).

Output

For each test case, the first and only line contains a single integer M - the answer.You may assume M<=1,000,000.

Example

Input:
1
3
1 3 4
2 7 3
3 2 1

Output:
6
Hints
-------------------------------------------------
| Year | Barb. No.1 | Barb. No. 2 | Barb. No. 3 |
-------------------------------------------------
|  0   |     1      |      2      |      3      |
-------------------------------------------------
|  1   |     4      |      3      |      5      |
-------------------------------------------------
|  2   |     1      |      4      |    Died     |
-------------------------------------------------
|  3   |     4      |      5      |    Died     |
-------------------------------------------------
|  4   |     1      |    Died     |    Died     |
-------------------------------------------------

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	5s
Source limit:	2048B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2002,Day 2; translated by Blue Mary

SPOJ Problem Set (classical)

1463. Robot Number M

Problem code: ROBOT

Blue Mary, the well-known astronaut, had sent Robot No.1 to Mars finally.Robot No.1 was so smart that he could make one robot per second.

Assume the time Robot No.1 arrived was second 1. At second i, Robot No.1 made a new Robot: Robot No.i. (i>=2)

The new robots started work as soon as he was produced successfully. Robot No.M only had a rest at second t, where t is a multiple of M. For example, Robot No.3 worked at second 4,5,7,8,... and had a rest at second 6,9,...

When a robot was having a rest, he could send his own informations to the newly produced robot. For example, when Robot No.6 was produced successfully, Robot No.2 and Robot No.3 are having a rest, so Robot No.6 would get informations from Robot No.2 and No.3. We call Robot No.2 and No.3 are teachers of Robot No.6.

We call two Robots are independent if each of them wasn't a teacher of the other one and they had no common teachers. Please note that Robot No.1 was independent to any other robots and wasn't a teacher of any other robots, since only Robot No.1 could make robots.

The good number of Robot No.M is the number of robots who was produced earlier than No.M and independent to No.M. Here are some examples:

The good number of Robot No.1 is 0.

The good number of Robot No.2 is 1. No.1 was that robot.

The good number of Robot No.6 is 2. No.1 and No.5 were those robots. No.2 and No.3 were his teachers. No.4 and him had a common teacher: No.2.

The Robots had 3 kinds of occupations. To Robot No.M:

If M can be written as the multiple of an even number of distinct odd primes, he was a businessman.
If M can be written as the multiple of an odd number(1 included) of distinct odd primes, he was a hacker.
All other robots were doctors.

Now Blue Mary was interesting to Robot No.M. She wants to know the sum of good numbers of all businessmen, hackers and doctors among Robot No.M and his teachers. She comes up with the answer quickly, and so can you.

Blue Mary is so kind that she gives you the prime divisors of M and you can only tell her the answers modudo 10000.

Input

The very first line contains a single integer T,the number of test cases.T blocks follow.

For each block, the first line contains a single integer K.K lines follow, each contains two integers p_i and a_i separated by a single space.

M = p₁^a₁ * p₂^a₂ * p₃^a₃ * ... * p_K^a_K.

You can assume that:

All p_i are distinct primes and are less than 10,000.
p₁ < p₂ < p₃ < ... n.
All a_i are positive and no more than 1,000,000.
1 <= k <= 1000.

Output

For each test case, output 3 lines.

The first line contains a single integer denotes to the sum of good numbers of all businessmen among Robot No.M and his teachers modudo 10000.

The second line contains a single integer denotes to the sum of good numbers of all hackers among Robot No.M and his teachers modudo 10000.

The third line contains a single integer denotes to the sum of good numbers of all doctors among Robot No.M and his teachers modudo 10000.

Example

Input:
1
3
2 1
3 2
5 1

Output:
8
6
75

Hints

In the sample input, M=2¹*3²*5¹=90. Robot No.90 has 10 teachers.Among Robot No.90 and his teachers, Robot No.15 is a businessman; No.3 and No.5 are hackers; all others are doctors, their numbers are 2,6,9,10,18,30,45,90.

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	2s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2002,Day 2; translated by Blue Mary

SPOJ Problem Set (classical)

1464. Editor II

Problem code: EDIT3

Background

After trying to solve problem EDIT1(Editor) and being ****ed by Brainf**k, Blue Mary decided to set another difficult problem about editor.

Description

Some definations:

Text: It's a sequence that consists characters whose ASCII code is in [32,126].
Cursor: It's a sign for pointing out the current position.It can be at the start or the end of the text or between two consecutive characters of the text.

Editor is a structure.It contains one text and one cursor.The operations are listed below:

--------------------------------------------------------------------------
| Name        | Input format |              function                     |
--------------------------------------------------------------------------
| Move(k)     | Move k       | Move the cursor after the kth character   |
|             |              | in the text. If k=0, you should put       |
|             |              | the cursor at the start of the text.      |
--------------------------------------------------------------------------
| Insert(n,s) | Insert n s   | Insert string s whose length is n(>=1)    |
|             |              | after the cursor.The cursor doesn't move. |
--------------------------------------------------------------------------
| Delete(n)   | Delete n     | Delete n(>=1) characters after the cursor.|
|             |              | The cursor doesn't move.                  |
--------------------------------------------------------------------------
| Get(n)      | Get n        | Output n(>=1) characters after the cursor.|
--------------------------------------------------------------------------
| Prev()      | Prev         |  Move the cursor one character forward.   |
--------------------------------------------------------------------------
| Next()      | Next         |  Move the cursor one character backward.  |
--------------------------------------------------------------------------

If the text of a editor is empty,we say the editor is empty.

Here is an example._ denotes to the cursor,$ denotes to the start and the end.At start the editor is empty.

------------------------------------------------------------------------------
|         Operation          |  Text after the operation |        Output     |
------------------------------------------------------------------------------
| INSERT(13,"Balanced tree") |  $_Balanced tree$         | $$                |
------------------------------------------------------------------------------
| MOVE(2)                    |  $Ba_lanced tree$         | $$                |
------------------------------------------------------------------------------
| DELETE(5)                  |  $Ba_d tree$              | $$                |
------------------------------------------------------------------------------
| NEXT()                     |  $Bad_ tree$              | $$                |
------------------------------------------------------------------------------
| INSERT(7," editor")        |  $Bad_ editor tree$       | $$                |
------------------------------------------------------------------------------
| MOVE(0)                    |  $_Bad editor tree$       | $$                |
------------------------------------------------------------------------------
| GET(15)                    |  $_Bad editor tree$       | $Bad editor tree$ |
------------------------------------------------------------------------------

Your task is:

Build an empty editor.
Read some operations from the standard input and operate them.
For each Get operation, write the answer to the output.

Input

the very first line contains the number of testcases T(T<=4).T tests follow.

For each test, the first line is the number of operations N.N operations follow.

Blue Mary is so depressed with the problem EDIT1 that she decides to make the problem more difficult.So she inserts many extra line breaks in the string of the Insert operation.You must ignore them.

Except line breaks, all the charaters' ASCII code are in [32,126]. There's no extra space at the end of a line.

You can assume that for each test case:

No invalid operation is in the input.
Number of move operations is no more than 50000.
Number of the total of insert and delete operations is no more than 4000.
Number of the total of prev and next operations is no more than 200000.
The characters inserted will not more than 2MB.The valid output will not more than 3MB.

Output

The output should contain T blocks corresponding to each testcase.

For each test case, the output should contain as many lines as the get operations in the input.Each line should contains the output of each get operation.

Example

Input:
1
15
Insert 26
abcdefghijklmnop
qrstuv wxy
Move 15
Delete 11
Move 5
Insert 1
^
Next
Insert 1
_
Next
Next
Insert 4
.\/.
Get 4
Prev
Insert 1
^
Move 0
Get 22

Output:
.\/.
abcde^_^f.\/.ghijklmno

Warning: large Input/Output data, be careful with certain languages

Blue Mary's note: the test case #1 has something wrong and it has been fixed on April 27th, 2007.Solutions has been rejudged. Please accept my apology.

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	3s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2003,Day 1

SPOJ Problem Set (classical)

1465. On the Way to Find Chris

Problem code: CHRIS

Do you know the famous game THE KING OF FIGHTERS? If the answer is yes, I'm sure you know THE THREE BLACK GROUP: Chris, Shermie and Yashiro. Today Chris is invited to one of his friends' home to play THE KING OF FIGHTERS.Blue Mary is now at Chris' home, she knows where Shermie's and Yashiro's home is, but she doesn't know where Chris actually is.So she decides that:

If Yashiro's home is nearer than Shermie's, she will go to Yashiro's home first, if she doesn't find Chris, she will then go to Shermie's, and vice versa.
The map of the city is strange. Each of the houses is assigned to a unique number in the range[1,n], where n is the number of houses. Between some pairs of houses there are some roads. There exists one and only one path from any house to any other house. She will go along the only path between the two houses.

Unfortunately, you don't know where Chris' home actually is, and the same as Yashiro's and Shermie's. Now you are interesting in the maximum time from the time when Blue Mary starts from Chris' home to the time when Blue Mary finds Chris in the worst case.

Input

The number of test cases T is given in the very first line.T blocks follow.

For each test case, the first line contains 2 space-separated integers N(3<=N<=200000) and M, which denotes the number of houses and the number of roads in the city.M lines follow, each contains 3 space-separated integers x,y,z(1<=x,y<=n,1<=z<=10⁹).It tells us there exist a road between house No.x and house No.y, and to go from x to y or from y to x along this road will take z minutes.No two roads are repeated.

Output

For each test case you should output a single line, which contains a single integer - the maximum time measured in minutes.

Example

Input:
1
4 3
1 2 1
2 3 1
3 4 1

Output
4

Warning: large Input/Output data, be careful with certain languages

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2003,Day 2; translated by Blue Mary

SPOJ Problem Set (classical)

1466. Blue Mary Needs Help Again

Problem code: CASHIER

Blue Mary is a cashier of a big company.The boss of this company is so annoying that he always increases or decreases wage of all workers.He increases all the workers' wage with a same number when he is happy or decreases all the worker's wage with a same number when he is depressed.

All the workers are angry with the boss, especially when he decreases their wage. A worker will leave the company and never go back when he finds his wage is lower than the least wage written on his contract. Blue Mary must delete the worker's files at that time. Another task she is to do is to build a file when a new worker joins this company.

The boss usually asks Blue Mary how much money the worker who gets the k-th most wage gets. Blue Mary is very tired with her work. Could you give her a hand?

Input

[the number of tests <= 10]

M MIN

[M is the number of commands below, MIN is the least wage]

C K

[C is one of the 4 characters I,A,S,F. I denotes that Mary should build a new file, and the new worker's wage is K(0<=K<=100000) at start.If K is less than MIN, the worker will not join the company. A denotes that the boss increases all the workers' wage with K(0<=K<=1000). S denotes that the boss decreases all the workers' wage with K(0<=K<=1000). F denotes that the boss asks Blue Mary a question: how much money does the worker who gets the k-th most wage get(K>0)?]

[M-1 other commands]

[other tests]

You may assume that:

The number of worker in the company at start is 0.
The number of command I is no more than 100000.
The total numner of command A and S is no more than 100.
The number of command F is no more than 100000.

Output

For each test case:

For each F command you must output one line contains a single integer which is the answer or -1 if K is more than the number of workers in the company at that time.

In the last line you must output a single integer - the number of workers who leave the company(excluded the ones who don't join the company)

Example

Sample Input:
1
9 10
I 60
I 70
S 50
F 2
I 30
S 15
A 5
F 1
F 2

Sample Output:
10
20
-1
2

Warning: large Input/Output data, be careful with certain languages

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	7s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2004,Day 1; translated by Blue Mary

SPOJ Problem Set (classical)

1468. Outside it is now raining

Problem code: RAIN2

Country M is pluvian. In City P, it rains frequently and many people complain that they always have trouble crossing the streets when raining. To make people cross the streets easier, the government set many "Automatic Umbrellas" above every crosswalk, shown in the picture below.

Each of these "Automatic Umbrellas" looks like a rectangle board, and their thickless is approximate zero. They can sop up the rain instantly. They are left unused when it's not raining and shuttle from one side to another in the same speed otherwise. The walkers will not be wringing-wet if he walks under the umbrella when it's raining.

When many people want to cross the street, one "Automatic Umbrella" is not enough obviously. The government set many "Automatic Umbrella" on some main crosswalks. The width of each of the "Automatic Umbrella" equals to the width of the crosswalk, and any two of these umbrellas have different height.Their length and speed may be different.

You are to write a program to calculate the total volume of the rain falling to the ground from the time when it starts to rain to T seconds later.

Input

The very first line comes a single integer Q, the number of test cases.Q blocks follow.

For each test case:

The first line contains 4 space-separated integers N(<=10), W(<=100), T(<=100), V(<=50), the number of "Automatic Umbrella", the length of the crosswalk in meters, the total time in seconds and the volume of rain falling to the ground per square meter per second.

To simplify the description, we can build a Cartesian coordinate system in the following way: let the left side of the street be the origin, the street be the positive Ox-axes, and the vertical line to the ground be the positive Oy-axes,see the picture below.

Each of the next N lines contains 3 integers xi, li, vi, the initial position(in meter), the length(in meter), the speed(in meter per second) of the i-th umbrella. If vi>0, the umbrella moves to the right side initially; if vi<0, the umbrella moves to the left side initially;if vi=0, the umbrella doesn't move at all.

You can assume that the width of the umbrella and the crosswalk is 1 meter, the rain falls vertically, the speed of the rain will not change and the umbrellas and the crosswalk are absolutely horizontal.

Output

For each test case, you should output a single real number(rounded to 2 decimal places) - the answer.You can assume the total distance of all the umbrella's movement will not exceed 550*W.

Example

Input:
1
2 4 3 10
0 1 1
3 1 -1

Output:
65.00

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	7s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2004,Day 2; translated by Blue Mary

SPOJ Problem Set (classical)

1470. Another Sequence Problem

Problem code: SEQ2

You are to write a program to perform some operations on a given sequence.These operations are listed below:

---------------------------------------------------------------------------------------------
| Name        | Input format   |              function                                      |
---------------------------------------------------------------------------------------------
| Modify      | MAKE-SAME i t c| Modify all the t numbers from the ith number(included) to  |
|             |                | number c.                                                  |
---------------------------------------------------------------------------------------------
| Insert      | INSERT i t s   | Insert t numbers after the ith number.s is a sequence of t |
|             |                | numbers which should be inserted one-to-one.If i=0,you     |
|             |                | should insert s in the first of the sequence.              |
---------------------------------------------------------------------------------------------
| Delete      | DELETE i t     | Delete t numbers after the ith number(included).           |
---------------------------------------------------------------------------------------------
| Reverse     | REVERSE i t    | Reverse t numbers after the ith number(included).          |
---------------------------------------------------------------------------------------------
| Get sum     | GET-SUM i t    | Output the sum of t numbers after the ith number(included).|
---------------------------------------------------------------------------------------------
| Get maximum | MAX-SUM        | Output the maximum partial sum in the sequence now.        |
| partial sum |                |                                                            |
---------------------------------------------------------------------------------------------

See the example.

Input

The very first line contains a single integer T(T<=4), the number of test cases.T blocks follow.

For each test case:

The first line contains two integers n and m(m<=20000), the number of numbers in the sequence in the beginning and the number of operations.

The second line contains n integers seperated by spaces, the sequence in the beginning.

Next m lines, each contains an operation listed above.

You can assume that for each test case:

No invalid operation is in the input.
Number of numbers in the sequence is no more than 500000 and not less than 1 at any time.
All the numbers in the sequence is in range[-1000,1000] at any time.
The total number of numbers inserted will be not more than 4,000,000.The input is no more than 20MB.

Output

For each Get sum and Get maximum partial sum operation,you should write the answer to the output,one per line.

Example

Input:
1
9 8
2 -6 3 5 1 -5 -3 6 3
GET-SUM 5 4
MAX-SUM
INSERT 8 3 -5 7 2
DELETE 12 1
MAKE-SAME 3 3 2
REVERSE 3 6
GET-SUM 5 4
MAX-SUM

Output:
-1
10
1
10

Hints:
After the 3rd op., the sequence is 
2 -6 3 5 1 -5 -3 6 -5 7 2 3

After the 4th op., the sequence is 
2 -6 3 5 1 -5 -3 6 -5 7 2

After the 5th op., the sequence is 
2 -6 2 2 2 -5 -3 6 -5 7 2

After the 6th op., the sequence is 
2 -6 6 -3 -5 2 2 2 -5 7 2

Warning: enormous Input/Output data, be careful with certain languages

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	7s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2005,Day 1; translated by lcosvse

SPOJ Problem Set (classical)

1471. A Game of Pearls

Problem code: PRLGAME

The game of pearls is to use the following 12 kinds of pearl designs each one and only one time to make the big pearl design.The pearl designs can be rotated and turned over arbitrarily. See the pictures below.


                   The empty grids



                  A sample big pearl design



A sample big pearl design used characters instead of colors



          Part A



          Part B



          Part C



          Part D



          Part E



          Part F



          Part G



          Part H



          Part I



          Part J



          Part K



          Part L

Input

Ten test cases(given one after another,you have to process all!), Each contains a big design, 'A'-'L' denote the filled grids, '.' denotes the empty grids,see the example. You can assume that the pearl designs used are completely put into the empty grids.

Output

A big design which has no grids that haven't been filled and each pearl design is used one and only one time in it,or 'No solution'(without quotes) if there's no solution.If there are multiple solutions,output any.

Example

Input:
.
..
...
....
.....
.....C
...CCC.
EEEHH...
E.HHH....
E.........
[and 9 test cases more]

Output:
B
BK
BKK
BJKK
JJJDD
GJGDDC
GGGCCCI
EEEHHIIA
ELHHHIAAF
ELLLLIFFFF
[and 9 test cases more]

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	20s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2005,Day 1; translated by Blue Mary

SPOJ Problem Set (classical)

1472. Tom and Jerry

Problem code: TOMJERRY

You may know the great American cartoon called Tom and Jerry. In that cartoon, Tom is a stupid cat, and Jerry is a cute mouse. They are all living in Blue Mary's house. (Maybe the name of the owner of the house they living in is not Blue Mary, but this is not important. ^_^)

One day Jerry gets a GPS, so after that he can detect Tom's position accurately. He decides to play tricks on Tom again. The house has N (1<= N <= 1000) rooms numbered from 1 to n and E(1<= E <=1000) corridors, each connects two different rooms, and there is at most one corridor between two rooms. When Jerry gets the GPS, he is in room No.P(1<= P <=N) while Tom is in room No.Q(1<= Q <= N). You may assume that room No.P and room No.Q is in one connected componenet and they are not the same room. Since Jerry is very cute and Tom is very stupid, if they are in the same room, Jerry can befool Tom as soon as possible. Now Jerry wants to get to Tom's room as soon as possible. At each time unit, he will detect Tom's position, and choose the room next to his room which is the nearest to Tom's position and go to that room. If there are several rooms satisfied the condition above, he will choose the one with the least room number. After that, if they are in the same room, Jerry will stay and play tricks on Tom, or he will repeat this progress one more time otherwise.

Now poor Tom doesn't know he'll be played, he is taking a walk in the house leisurely. Each time unit he will choose a room next to the room he is in and go to that room or stay in the room he is in now, with equal probability. For example, if Tom is now in room 1, room 2 and room 3 are the only neighbors of room 1 (i.e. there is a corridor between room 1 and room 2, and there is a corridor between room 1 and room 3), at the next time unit, the probability of that Tom is in room 1,2 or 3 are all 1/3.

Suppose at each time unit, Jerry moves first, and Tom will move after Jerry complete his move. You task is to calculate the expected time unit from the time when Jerry gets the GPS to the time when Jerry and Tom are in the same room.

Input

Multiple test cases, the number of them is given in the very first line.

For each test case:

The first line contains two space-separated integers N and E. The second line contains two space-separated integers P and Q. E lines then follow, each contains 2 space-separated integers A and B which shows that there is a corridor between room A and room B.

Output

For each test case:

Output one line, which contains a single real number - the expected time unit, rounded to 3 decimal places.

Example

Input:
2
4 3
1 4
1 2
2 3
3 4
9 9
9 3
1 2
2 3
3 4
4 5
3 6
4 6
4 7
7 8
8 9

Output:
1.500
2.167

Hint
The calculations for the first example can be found here.

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	6s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2005,Day 2; translated by Blue Mary

SPOJ Problem Set (classical)

1473. Lemon Tree in the Moonlight

Problem code: LEMON

Blue Mary extremely like lemon trees. When the softness moon shines the ground, she lies under the lemon tree, thinking about the true meaning of life, the universe and everything quietly.

Before long, she is shadowed by the lemon tree. Blue Mary is such a cute girl, that she soon comes up with a question: what is the area of the shadow?

She knows it's hard for her to measure the shadow directly. So that, she tries to calculate it in geometrical way.

As Mary knows well about this beautiful lemon tree, she regards it as N frustums of cones,each frustums of cone is defined as a floor, numbered 1..N from the bottom to top. Of course, the Nth(Top) is a cone. Each frustum has two circle surfaces. Each two adjacent frustums shares a same circle surface. All the centres of the circle surfaces are on a plumb line. Mary knows that the height of every frustums is h1,h2,..,hn, and the undersurface of the 1st frustum has a height h0 from the ground.

Mary measures that the included angle of the moonshine and the ground is Alpha, which is an acute angle.

For briefness, we suppose the moonshine is parallel and the ground is aclinic.

And we ignore the bole of the tree. Mary comes up with the answer quickly, and she wants your ideas all the same.

Input

The very first line of the input data contains one integer T, the number of tests. T blocks follow.

For each test:

The first line of the input data contains one integer number N(N<=500) and a real number Alpha (Alpha>0.3).

N denote the number of floors, Alpha denote the included angle of the moonshine and the ground(radian).

The second line contains N + 1 real number h0 h1 h2... hn.(hi<=100) h0 denotes the height of the undersurface of the 1st frustum. h1 .. hn denote the height of each floor.

The third line contains N real number r1 r2 .. rn(ri<=100), the radii of the undersurface in each floor.

All the data in each line is seperated by spaces.

Output

For each data set you should output one line containing a single real number - the area of the shadow. Numbers should be rounded to two decimal places.

Example

Input:
1
2 0.7853981633
10.0 10.00 10.00
4.00 5.00

Output:
171.97

Time limit has been changed from 30 seconds to 13 seconds, some naive solution gets TLE.

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	13s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2005,Day 2; translated by g201513

SPOJ Problem Set (classical)

1475. VII - Act IV

Problem code: WORMS

Background

This problem is completely unrelated to its problem code ^_^.

Description

A natural number x is called a good number if one or two of the next two conditions is satisfied:

7 is a divisor of x.
7 is a digit of x.

Task

Write a program that:

reads a number n from the standard input,
computes the number of good numbers in range[1,10ⁿ],
writes the result to the standard output.

Solve the problem in at most 0.5kB of source code.

Input

The input begins with an integer t(t<= 210), the number of test cases.t test cases follow.

For each test case, the first and only line contains an integer n (1<=n<=500).

Output

For each test case the output consists of one line that contains the answer.

Example

Sample input:
3
1
2
1

Sample output:
1
30
1

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	2s
Source limit:	512B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Folklore, description, standard program and test data by Blue Mary

SPOJ Problem Set (classical)

1476. Maximum Profit

Problem code: PROFIT

CS&T, the well-known cellphone company, is going to set some new service stations among n possible ones, which are numbered 1,2,...,n. The costs of setting these stations are known as P1,P2,..,Pn. Also the company has made a survey among the cellphone users, and now they know that there are m user groups numbered 1,2,...,m, which will communicate by service station Ai and Bi, and the company can profit Ci.

Now CS&T wants to know which service stations are to be set that the company will profit most.

Input

T [The number of tests]
n m [n<=5000 m<=50000]
P1 P2 P3 ... Pn [Pi<=100]
A1 B1 C1 
A2 B2 C2
...
Am Bm Cm [1<=Ai,Bi<=n, Ci<=100]
[other tests]
At least 80% of the tests satisfy that n<=200, m<=1000.

Output

MaximumProfit
[other tests]

Example

Input:
1
5 5
1 2 3 4 5
1 2 3
2 3 4
1 3 3
1 4 2
4 5 3

Output:
4
Hints:
The service stations to be set are 1,2,3.

Added by:	[Trichromatic] XilinX
Date:	2007-04-01
Time limit:	7s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2006,Day 2; translated by Blue Mary

SPOJ Problem Set (classical)

1477. Play with a Tree

Problem code: PT07A

Hey, ACRush and Jelly are playing a game ! Let take a look at its rule:

You are given a tree. Two players take turns cutting edges on a tree. Some nodes is on the "ground". When a player cuts an edge, all the edges that are no longer connected to the ground disappear. The player who can not take a move loses.

ACRush plays first. Both of them are very good players. If you know state of the tree they are playing with, can you guess who will win?

Node 4 is on the ground.

Input

Input consists of multiple test-cases. The first line contains one integer t - number of cases (0 < t <= 20). For each case, the input format is following. The first line contains one integer N (1 <= N <= 100000). The next line N integers s[i] (1 or 0). If s[i] is 1, the i-th node is on the ground. If s[i] is 0, the i-th node is not on the ground. Each line of the following N - 1 lines contains two integers u, v. They denote there is an edge between node u and node v (1 <= u,v <= N).
There is no blank line after each case.

Output

For each case, output who will win the game. If ACRush wins, output 1; otherwise, output 0 (Jelly wins).
There is no blank line after each case.

Example

Input:
1
4
0 0 0 1
1 2
2 3
2 4

Output:
1

Added by:	Thanh-Vy Hua
Date:	2007-04-07
Time limit:	0.5s-1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Co-author Amber

SPOJ Problem Set (classical)

1478. The Easiest Problem

Problem code: PT07B

You are given an unweighted, undirected tree T. We say T is special iff it has this property:

"All nodes of degree greater than or equal to 3 are surrounded by at most two nodes of degree two or greater."

Finding maximal size subtree of this tree so that it's a special tree.

Input

The first line of the input file contains one integer N --- number of nodes in the tree (0 < N <= 10⁶). Next N-1 lines contain N-1 edges of that tree --- Each line contains a pair (u, v) means there is an edge between node u and node v (1 <= u, v <= N).

Output

At the first line, output number of nodes in the optimal subtree you found. Next lines, print all edges belong to that subtree, each line contains a pair u v means an edge between node u and node v.

Example

Input:
5
1 2
2 3
2 4
2 5

Output:
5
1 2
2 3
2 4
2 5

Added by:	Thanh-Vy Hua
Date:	2007-04-07
Time limit:	0.100s-10s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Co-author Amber

SPOJ Problem Set (classical)

1479. The GbAaY Kingdom

Problem code: PT07C

Jiajia is the king of the GbAaY Kingdom. He always squeezes his 20 ministers as coolies. There are n cities and m two-way roads connecting cities in the kingdom. Because of the increasing of the oil fee, he want to simplify the road system in the GbAaY Kingdom to save the traffic cost. Thus, some of roads will be removed. But he requests the ministers guarantee that there is always a path between any two cities. GbAaY Minister Loner suggests Jiajia for the convenience of the traffic management, the farthest distance between cities should be minimal. Unhesitatingly, Jiajia agrees this resolution. As the GbAaY Kingdom's minister (cooly), you must work hard for Jiajia to make the simplification plan.

Input

The first line contains two integers n, m (1 <= n <= 200, n - 1 <= m <= 20000). Each line of the following m lines contains three integers u, v, w (u != v, 0 <= w <= 10⁵). They denote there is a road with length w between city u and city v.

Output

The first line contains one integer which is the farthest distance between cities after the simplification. Each line of the follow n - 1 contains two integers u, v (u < v). They denote there is an road between city u and city v in the simplification plan. If there are many optimal solutions, any of them will be accepted.

Example

Input:
3 3
1 2 1
2 3 1
1 3 1

Output:
2
1 2
1 3

Added by:	Thanh-Vy Hua
Date:	2007-04-07
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS
Resource:	Co-author Amber

SPOJ Problem Set (main)

1480. Let us count 1 2 3

Problem code: PT07D

Given two integer n, p. 4 kinds of query is needed to solve:

1. Counting the number of labeled unrooted trees with n nodes
2. Counting the number of labeled rooted trees with n nodes
3. Counting the number of unlabeled rooted trees with n nodes
4. Counting the number of unlabeled unrooted trees with n nodes
Calculate the answer modulo p.

Input

Each line contains three integers k, n, p. k denotes which kind of query this case is.
For Kind 1 or Kind 2 query, 1 <= n <= 10⁹.
For Kind 3 or Kind 4 query, 1 <= n <= 10³ and n <= p.
For all queries, 2 <= p <= 10⁴ and p is a prime.

Output

For each query, output a line which contains only one integer.

Example

Input:
1 2 2
2 2 3
3 2 5
4 2 3

Output:
1
2
1
1

Added by:	Thanh-Vy Hua
Date:	2007-04-07
Time limit:	0.300s-4s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	Co-author Amber

SPOJ Problem Set (main)

1482. A short vacation in Disneyland

Problem code: PT07F

After a lot of exams at school, Amber and his friends Ahyangyi, Dragon have a short vacation in Hong Kong Disneyland. Many interesting places they want to visit there: resort, castle,... . In each place and between them, there are special bidirectional rails, so that the visitors can drive a small special car, go around and have a sightseeing tour. This rail system is quite optimal it has tree shape ! Each time, you start a new route (or you can call it "path") with a car, you must purchase a new ticket.

Amber and his friends surely want to visit all places, and each place exactly once, so bored to visit one place many times. But the trouble is they don't carry much money. So Amber thinks about a good way to purchase as small number of tickets as possible (i.e. minimal number of routes). We don't care how they can switch cars during their trip.

Now you're given maps of the Disneyland, please help them to find an optimal solution.

Take a look at the figure below:

There are many optimal solutions here and Amber must purchase at least 3 tickets, for 3 disjoint routes. Two possible solutions are:
Solution 1:
1-st route: they visit 1 2 3
2-nd route: they visit 4
3-rd route: they visit 5 6 7
Solution 2:
1-st route: they visit 1 2 4 6 5
2-nd route: they visit 3
3-rd route: they visit 7

Input

There may be many maps in one input file. The first line of file is number of maps T (0 < T <= 10). The following line is blank. Then, there are the descriptions of T maps.

For each map, the first line contains one integer N --- number of places in the Disneyland (0 < N <= 10000). We number places from 1 to N. Next N-1 lines contain N-1 rails between places --- Each line contains a pair (u, v) means there is a rail between place u and place v (1 <= u,v <= N).
There is a blank line after each description.

Output

For each map, the first line, write minimal number of routes K. Next K lines, show out the routes in your solution, each has form u[1] u[2]...u[m], means the route starts at place u[1] then visits place u[2],..., ends at place u[m]. So between 2 consecutive places in each route must have a rail. If there are many solutions, any of them will be accepted.
There is no blank line after each case.

Example

Input:
1

7
1 2
2 3
2 4
4 6
5 6
6 7

Output:
3
1 2 3
4
5 6 7

Added by:	Thanh-Vy Hua
Date:	2007-04-07
Time limit:	0.100s-0.5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	Co-author Amber

SPOJ Problem Set (main)

1483. Colorful Lights Party

Problem code: PT07G

ACRush and his friends want to open a party to celebrate the good result of THU in ICPC 2007. They will use all halls in THU for their party. There are 2 kinds of hall: the small and the large one. In each hall, there is an electronic light system, which forms a tree topology to reduce redundant wires.

In a small hall, the light system is a general tree with n lights. The lights are numbered from 1 to n
In a large hall, the light system is obtained from k chains of lights, each chain has length t. The first lights of these k chains are connected with a big light at the central stage of the hall. The big light has id 1, the first light of each chain has id from 2 to k+1, then we continue with the second light of each chain, so on...

Take a look at the figure below:

ACRush hopes in every hall, each light has an unique color and so do the wires!

For easier to remember and to hang up lights against the walls, he sets a rule:

For each hall, we number the color from 0 to n-1, so each light will get a color id in set {0, 1, ..., n-1}.
Color id of the wire connects i-th light and j-th light uniquely identified by the positive difference between color ids of i-th light and j-th light.

At first view, the rule seems easy, so everyone agrees with him. But it's really tough if the room is quite large, too hard to set colors for lights. After few seconds, ACRush says "So in this hall, the 1-st light should have color 3, the 2-nd one should have color 0,...". Well, how can he do it very fast?

How about you ? Let write a program to help ACRush's friends setting colors for lights in all T halls.

Input

The first line of file is T -- number of halls in THU (0 < T <= 10). The following line is blank. Then, there are the descriptions of T halls.

For each hall, the first line contains one integer kind. kind denotes which kind of the current hall: 1 is a small hall, 2 is a large one. On next line, there are two cases:

For Kind 1, first line is n (1 <= n <= 27) -- number of lights. Next n - 1 lines describe wires in this hall. Each line is pair (u, v) -- there is a wire between light u and v (1 <= u, v <= n).
For Kind 2, only one line contains two numbers k and t (1 <= k, t <= 1000).

There is a blank line after each description.

Output

For each hall, show us n numbers on one line, i-th number is the color id of i-th light. If there are many solutions any of them will be accepted. Otherwise, if there is no solution, all color id should be -1.
The color ids on one line are separated by exactly one blank, and you'd better not print any redundant blanks. There is no blank line after each case.

Example

Input:
2

1
3
1 2
2 3

2
2 1

Output:
0 2 1
0 4 2 1 3

Added by:	Thanh-Vy Hua
Date:	2007-04-07
Time limit:	0.100s-2s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	Co-author Amber

SPOJ Problem Set (main)

1484. Search in XML

Problem code: PT07H

The XML (eXtensible Markup Language) is gaining popularity as a new standard for data representation and exchange on the internet. XML provides a text-based means to describe and apply a tree-based structure to information. The XML document consists of nested elements, some of which usually have attributes and content. But for simplifying this problem, we needn't consider the attributes and content, i.e. only tags allowed. An element typically consists of two tags, a start tag and an end tag. The start tag consists of a name surrounded by angle brackets, like "<tag>"; the end tag consists of the same name surrounded by angle brackets, but with a slash preceding the name, like "</tag>". The element's content is empty or other sub-element (child) that appears between the start tag and the end tag. Specially, no XML element that has the same tag in its direct sub-elements (children), i.e. All sibling elements have different tag names. The following is an valid example for XML documents.

<THU>
	<Team>
		<ACRush></ACRush>
		<Jelly></Jelly>
		<Cooly></Cooly>
	</Team>
	<JiaJia>
		<Team>
			<Ahyangyi></Ahyangyi>
			<Dragon></Dragon>
			<Cooly><Amber></Amber></Cooly>
		</Team>
	</JiaJia>
</THU>

For identifying the elements in a document, we number the elements in according to the order that the start tags of the elements appear in the document. For instances, "THU" is numbered 1. The first "Team" is numbered 2. "ACRush" is numbered 3. "Ahyangyi" is numbered 8.

The problem of querying XML documents has been given much attention by researchers. Now we are given a querying pattern of XML documents and a text of XML documents. The following is an valid example for pattern.

<Team><Cooly></Cooly></Team>

And we are requested to find all occurrences of the pattern in the text of XML documents. Here, the pattern occurs at a particular text position if placing the pattern with root element at that text position leads to a situation in which each pattern element overlaps some text element with the same label. Because the sibling elements have different labels, there is only one way to put the pattern into the text.

Input

There are two parts in the input file. The first part is a valid XML documents with exactly one root element. The second part is a valid XML documents as querying pattern with exactly one root element. Please ignore all whitespaces (unvisiable characters) in the input file, i.e. only consider the uppercase and lowercase letter and "/", "<", ">". Assume XML documents is always strictly a rooted tree. The input file is less than 100kb.

Output

Output all the occurrences of pattern in a text of XML documents. The first line consists of an integer n that denotes the number of the occurrences. Then the next n line, each line consists of an id number of an element that occurs the query pattern. Please print them in increasing order.

Example

Input:
<THU>
	<Team>
		<ACRush></ACRush>
		<Jelly></Jelly>
		<Cooly></Cooly>
	</Team>
	<JiaJia>
		<Team>
			<Ahyangyi></Ahyangyi>
			<Dragon></Dragon>
			<Cooly><Amber></Amber></Cooly>
		</Team>
	</JiaJia>
</THU>
<Team><Cooly></Cooly></Team>

Output:
2
2
7

Added by:	Thanh-Vy Hua
Date:	2007-04-07
Time limit:	0.100s-3s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	Co-author Amber

SPOJ Problem Set (main)

1487. Query on a tree III

Problem code: PT07J

You are given a node-labeled rooted tree with n nodes.

Define the query (x, k): Find the node whose label is k-th largest in the subtree of the node x. Assume no two nodes have the same labels.

Input

The first line contains one integer n (1 <= n <= 10⁵). The next line contains n integers l_i (0 <= l_i <= 10⁹) which denotes the label of the i-th node.

Each line of the following n - 1 lines contains two integers u, v. They denote there is an edge between node u and node v. Node 1 is the root of the tree.

The next line contains one integer m (1 <= m <= 10⁴) which denotes the number of the queries. Each line of the next m contains two integers x, k. (k <= the total node number in the subtree of x)

Output

For each query (x, k), output the index of the node whose label is the k-th largest in the subtree of the node x.

Example

Added by:	Thanh-Vy Hua
Date:	2007-04-07
Time limit:	1s-1.100s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	Co-author Amber

SPOJ Problem Set ()

1505. Whac-a-Mole

Problem code: MOLE

Map While visiting a traveling fun fair you suddenly have an urge to break the high score in the Whac-a-Mole game. The goal of the Whac-a-Mole game is to... well... whack moles. With a hammer. To make the job easier you have ﬁrst consulted the fortune teller and now you know the exact appearance patterns of the moles. The moles appear out of holes occupying the n² integer points (x, y) satisfying 0 ≤ x, y <n in a two-dimensional coordinate system. At each time step, some moles will appear and then disappear again before the next time step. After the moles appear but before they disappear, you are able to move your hammer in a straight line to any position (x2 , y2 ) that is at ditance at most d from your current position (x1 , y1 ). For simplicity, we assume that yo can only move your hammer to a point having integer coordinates. A mole is whacke if the center of the hole it appears out of is located on the line between (x1 , y1 ) an (x2 , y2 ) (including the two endpoints). Every mole whacked earns you a point. Whe the game starts, before the ﬁrst time step, you are able to place your hammer anywher you see ﬁt.

Input

The input consists of several test cases. Each test case starts with a line containing three integers n, d and m, where n and d are as described above, and m is the total number of moles that will appear (1 ≤ n ≤ 20, 1 ≤ d ≤ 5, and 1 ≤ m ≤ 1000). Then follow m lines, each containing three integers x, y and t giving the position and time of the appearance of a mole (0 ≤ x, y < n and 1 ≤ t ≤ 10). No two moles will appear at the same place at the same time. The input is ended with a test case where n = d = m = 0. This case should not be processed.

Output

For each test case output a single line containing a single integer, the maximum possible score achievable.

Example

Added by:	Abhilash I
Date:	2007-04-19
Time limit:	5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6

SPOJ Problem Set (classical)

1526. Ranklist Sorting

Problem code: RSORTING

You are given the scores of several players in a competition. Your task is to create a ranklist of the players, sorted in decreasing order by score.

Unfortunately, the data structure used for the list of players supports only one operation, which moves a player from position i to position j without changing the relative order of other players. If i > j, the positions of players at positions between j and i − 1 increase by 1, otherwise if i < j the positions of players at positions between i + 1 and j decrease by 1.

This operation takes i steps to locate the player to be moved, and j steps to locate the position where he or she is moved to, so the overall cost of moving a player from position i to position j is i + j. Here, positions are numbered starting with 1.

Determine a sequence of moves to create the ranklist such that the sum of the costs of the moves is minimized.

Input

The input consists of exactly 10 test cases. The first line of each test case contains n (2 ≤ n ≤ 1000), the number of players. Each of the following n lines contains one non-negative integer s_i (0 ≤ s_i ≤ 1000000), the scores of the players in the current order. You may assume that all scores are distinct.

Output

For each test case, print in one line the number of moves used to create the ranklist. The following lines should specify the moves in the order in which they are applied. Each move should be described by a line containing two integers i and j, which means that the player at position i is moved to position j. The numbers i and j must be separated by a single space.

Example

here only one test case

Input:
5
20
30
5
15
10

Output:
2
2 1
3 5

Added by:	Adrian Kuegel
Date:	2007-05-04
Time limit:	4s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	own problem, used in BOI 2007

SPOJ Problem Set (classical)

1536. Help Blue Mary Please! (Act III)

Problem code: BLUEEQ3

Background

This morning Blue Mary wrote some equations on a piece of paper and left it on her desk.After solving some problems in SPOJ,she found that her classmate H.L. replaced all characters on the paper with some other ones.H.L. told her he replaced the same characters with the same ones,and different characters with different ones because of his goodness.Now Mary needs your help to get the original equations back.(See problem BLUEEQ)

Input

Ten test cases(given one after another,you have to process all!)For each test case, the first line is a single integer n(n<=21).Next 3 lines contains 3 strings, each of them has a length of n and contains only first n capital latin characters.The sum of the numbers the first two strings indicates equals to the number the third string incicates.The numbers can have leading zeros and each of their bases is n.

Output

For each test case you should output one line contains n numbers separated by spaces, which is a permutation of integer numbers 0 to n-1.Number x is on the k-th position iff x is replaced by the kth capital latin character.There is one and only one solution for each test case.

Example

Input:
5
ABCED
BDACE
EBBAA
[and 9 test cases more]
Output:
1 0 3 4 2
[and 9 test cases more]

Added by:	[Trichromatic] XilinX
Date:	2007-05-08
Time limit:	17s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	description by Blue Mary

SPOJ Problem Set (classical)

1538. Making Jumps

Problem code: MKJUMPS

A knight is a piece used in the game of chess. The chessboard itself is square array of cells. Each time a knight moves, its resulting position is two rows and one column, or two columns and one row away from its starting position. Thus a knight starting on row r, column c – which we’ll denote as (r,c) – can move to any of the squares (r-2,c-1), (r-2,c+1), (r-1,c-2), (r-1,c+2), (r+1,c-2), (r+1,c+2), (r+2,c-1), or (r+2,c+1). Of course, the knight may not move to any square that is not on the board.

Suppose the chessboard is not square, but instead has rows with variable numbers of columns, and with each row offset zero or more columns to the right of the row above it. The figure to the left illustrates one possible configuration. How many of the squares in such a modified chessboard can a knight, starting in the upper left square (marked with an asterisk), not reach in any number of moves without resting in any square more than once?

If necessary, the knight is permitted to pass over regions that are outside the borders of the modified chessboard, but as usual, it can only move to squares that are within the borders of the board.

Input

There will be multiple cases to consider. The input for each case begins with an integer n, between 1 and 10, that specifies the number of rows in the modified chessboard. Following n there will be n pairs of integers, with the ith pair corresponding to the ith row of the chessboard. The first integer of each pair indicates the number of squares skipped at the beginning of the row. The second integer indicates the number of squares in the row (which will always be at least 1).The last case will be followed by the integer 0.

For example, input for the case illustrated by the chessboard shown above would be:

7 0 3 0 3 0 4 0 4 1 3 1 7 4 4

The maximum dimensions of the board will be 10 rows and 10 columns. That is, any modified chessboard specified by the input will fit completely on a 10 row, 10 column board.

Output

For each input case, display the case number (1, 2, …), and the number of squares that the knight can not reach. Display the results in the format shown in the examples below.

Example

Input:
7 0 3 0 3 0 4 0 4 1 3 1 7 4 4
3 0 3 0 3 0 3
2 0 1 2 1
0

Output:
Case 1, 4 squares can not be reached.
Case 2, 1 square can not be reached.
Case 3, 0 squares can not be reached.

Added by:	Camilo Andrés Varela León
Date:	2007-05-11
Time limit:	5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	North Central North America Regional Programming Contest - 2003

SPOJ Problem Set (classical)

1552. Mobiles

Problem code: MOBILE2

You have been asked to buy a gift for your baby brother, Ike. However, you have noticed that Ike has a very particular taste in gifts. He only likes gifts that are configured in his particular style.

You have found a shop that sells mobiles. A mobile is a multi-layered decoration that is typically hung from the roof. Each mobile consists of a series of horizontal rods connected by vertical wires. Each rod has a wire hanging from both ends, which holds either another horizontal rod or a toy.

A sample mobile is shown below:

To satisfy your brother, you need to find a mobile that can be reconfigured so that:

(i) any two toys are either at the same level (that is, joined to the roof by the same number of rods), or di.er by only one level;

(ii) for any two toys that differ by one level, the toy to the left is further down than the toy to the right.

Mobiles can be reconfigured by performing swaps. A swap involves taking some rod, unhooking whatever is hanging beneath the left and right ends, and reattaching them at opposite ends (that is, the right and left ends respectively). This process does not modify the ordering of any rods or toys further down.

Since you are training for the Informatics Olympiad, you decide to write a program to test whether a given mobile can be reconfigured into a gift that Ike will like!

As an example, consider the mobile illustrated earlier. Ike will not like this mobile. Although it satisfies condition (i), it breaks condition (ii) — the toy at the leftmost end is at a higher level than the toys to its right.

However, the mobile can be reconfigured into a mobile that Ike will like. The following swaps are required:

1. First, the left and right ends of rod 1 are swapped. This exchanges the positions of rods 2 and 3, resulting in the following configuration:

2. Second, and finally, the left and right ends of rod 2 are swapped. This moves rod 4 to the left end of rod 2, and the toy to the right end of rod 2.

It can be seen that this final mobile satisfies Ike's requirements. All toys are at most one level apart, and the toys at a lower level are further to the left than the toys at a higher level.

Your task is, given a description of a mobile, to determine the smallest number of swaps required to reconfigure it so that Ike will like it (if this is possible). You may assume that the toys can never get in each other's way.

Input

Multiple test cases, the number of them will be given at the very first line.

For each test case:

The first line of input will contain the single integer n (1 <= n <= 100 000) representing the number of rods in the mobile. The rods are numbered 1, 2 , ..., n.

The following n lines will describe the connections for each rod. Specifically, the ith of these lines will describe rod i. Each of these lines will contain two integers l r separated by a single space, indicating what is hung beneath the left and right ends of the rod respectively. If a toy is hung beneath this rod, the corresponding integer l or r will be -1. Otherwise the integer l or r will be the number of a rod that is hung beneath this rod.

If there are any rods hanging beneath rod i, these rods will have numbers strictly greater than i. Rod 1 is the single rod at the top of the mobile.

Output

Output should consist of a single line containing a single integer, giving the smallest number of swaps required to reconfigure the mobile according to Ike's constraints. If this is not possible, you should output the integer -1.

Example

Input:
1
6
2 3 
-1 4 
5 6 
-1 -1 
-1 -1 
-1 -1 

Output:
2

Warning: large input/output data,be careful with certain languages

Added by:	[Trichromatic] XilinX
Date:	2007-05-14
Time limit:	17s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Asia-Pacific Informatics Olympiad(APIO) 2007

SPOJ Problem Set (classical)

1553. Backup Files

Problem code: BACKUP

You run an IT company that backs up computer data for large offices. Backing up data is not fun, and so you design your system so that the different offices can back up each others' data while you sit at home and play computer games instead.

The offices are all situated along a single street. You decide to pair up the offices, and for each pair of offices you run a network cable between the two buildings so that they can back up each others' data.

However, network cables are expensive. Your local telecommunications company will only give you k network cables, which means you can only arrange backups for k pairs of offices (2k offices in total). No office may belong to more than one pair (that is, these 2k offices must all be different). Furthermore, the telecommunications company charges by the kilometre. This means that you need to choose these k pairs of offices so that you use as little cable as possible. In other words, you need to choose the pairs so that, when the distances between the two offices in each pair are added together, the total distance is as small as possible.

As an example, suppose you had five clients with offices on a street as illustrated below. These offices are situated 1 km, 3 km, 4 km, 6km and 12km from the beginning of the street. The telecommunications company will only provide you with k = 2 cables.

The best pairing in this example is created by linking the first and second offices together, and linking the third and fourth offices together. This uses k = 2 cables as required, where the first cable has length 3km - 1km = 2 km, and the second cable has length 6km - 4km = 2 km. This pairing requires a total of 4km of network cables, which is the smallest total possible.

Input

Multiple test cases, the number of them will be given at the very first line.

For each test case:

The first line of input will contain the integers n and k, representing the number of offices on the street (2 <= n <= 100 000) and the number of available network cables (1 <= k <= n/2).

The following n lines will each contain a single integer (0 <= s <= 1 000 000 000), representing the distance of each office from the beginning of the street. These integers will appear in sorted order from smallest to largest. No two offices will share the same location.

Output

Output should consist of a single positive integer, giving the smallest total length of network cable required to join 2k distinct offices into k pairs.

Example

Input: 1 5 2 1 3 4 6 12 Output: 4 Explanation

The sample input above represents the example scenario described earlier.

Warning: large input/output data,be careful with certain languages

Blue Mary's Note: test data has been modified on Dec. 5, 2007. All the solutions have been rejudged.

Added by:	[Trichromatic] XilinX
Date:	2007-05-14
Time limit:	17s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Asia-Pacific Informatics Olympiad(APIO) 2007

SPOJ Problem Set (classical)

1554. Zoo

Problem code: ZOO

The pride of the Asia-Pacific region is the newly constructed Great Circular Zoo. Situated on a small Pacific island, it consists of a large circle of different enclosures, each containing its own exotic animal as illustrated below.

You are in charge of public relations for the zoo, which means it is your job to keep people as happy as possible. A busload of schoolchildren has just arrived, and you are eager to please them. However, this is no easy task|there are animals that some children love, and there are animals that some children fear. For example, little Alex loves monkeys and koalas because they are cute, but fears lions because of their sharp teeth. On the other hand, Polly loves lions because of their beautiful manes, but fears koalas because they are extremely smelly.

You have the option of removing some animals from their enclosures, so that children are not afraid. However, you are worried that if you remove too many animals then this will leave the children with nothing to look at. Your task is to decide which animals to remove so that as many children can be made happy as possible.

Each child is standing outside the circle, where they can see five consecutive enclosures. You have obtained a list of which animals each child fears, and which animals each child loves. A child will be made happy if either at least one animal they fear is removed from their field of vision, or at least one animal they love is not removed from their field of vision.

For example, consider the list of children and animals illustrated below:

-----------------------------------------------------------------------
|Child      |Enclosures Visible |Fears                |Loves          |
|Alex       |2, 3, 4, 5, 6      |Enclosure 4          |Enclosures 2, 6|
|Polly      |3, 4, 5, 6, 7      |Enclosure 6          |Enclosure 4    |
|Chaitanya  |6, 7, 8, 9, 10     |Enclosure 9          |Enclosures 6, 8|
|Hwan       |8, 9, 10, 11, 12   |Enclosure 9          |Enclosure 12   |
|Ka-Shu     |12, 13, 14, 1, 2   |Enclosures 12, 13, 2 |-              |
-----------------------------------------------------------------------

Suppose you remove the animals from enclosures 4 and 12. This will make Alex and Ka-Shu happy, because at least one animal that they fear has gone. This will also keep Chaitanya happy, since both enclosures 6 and 8 still contain animals that he loves. However, both Polly and Hwan will be unhappy, since they cannot see any animals that they love but they can still see all the animals that they fear. This arrangement therefore gives a total of three happy children.

Now suppose you put these animals back into their enclosures, and remove the animals from enclosures 4 and 6 instead. Alex and Polly will be happy because the animals that they fear in enclosures 4 and 6 have gone. Chaitanya will be happy because, even though animal 6 has gone, he can still see the animal in enclosure 8 which he loves. Likewise, Hwan will be happy because she can now see the animal in enclosure 12, which she loves. The only person unhappy will be Ka-Shu.

Finally, suppose you put the animals back once more and then remove only the animal from enclosure 13. Ka-Shu will now be happy since one animal that he fears has been removed, and Alex, Polly, Chaitanya and Hwan will all be happy since they can all see at least one animal that they love. Thus this arrangement gives five happy children, the largest number possible.

Input

Multiple test cases, the number of them will be given at the very first line.

For each test case:

The first line will be of the form N C, where N is the number of animal enclosures (10 <= N <= 10 000) and C is the number of children (1 <= C <= 50 000). The enclosures are numbered 1, 2, ...,N clockwise around the circle.

Following this will be C additional lines of input, where each line describes a single child. Each of these lines will be of the form:

E F L X1 X2 ... XF Y1 Y2 ... YL;

where:

E is the first enclosure that the child can see (1 <= E <= N). In other words, the child can see enclosures E, E + 1, E + 2, E + 3 and E + 4. Note that numbers larger than N wrap back around the circle, so if N = 14 and E = 13 then the child can see enclosures 13, 14, 1, 2 and 3.
F is the number of animals that the child fears, and L is the number of animals that the child loves.
Enclosures X1,...,XF contain the animals that the child fears (1<=X1,...,XF<=N).
Enclosures Y1,...,YL contain the animals that the child loves (1<=Y1,...,YL<=N).
No two of the integers X1,...,XF,Y1,...,YL are equal, and all of these integers describe enclosures that the child can see.

Children will be listed in sorted order according to the first enclosure E (so the child with lowest E will appear first and the child with largest E will appear last). Note that more than one child may have the same first enclosure E.

Output

Output must consist of a single integer, giving the largest number of children that can be made happy.

Example

Sample Input: 2 14 5 2 1 2 4 2 6 3 1 1 6 4 6 1 2 9 6 8 8 1 1 9 12 12 3 0 12 13 2 12 7 1 1 1 1 5 5 1 1 5 7 5 0 3 5 7 9 7 1 1 7 9 9 1 1 9 11 9 3 0 9 11 1 11 1 1 11 1 Sample Output: 5 6 Explanation:

The first sample case is the example discussed earlier, in which all C = 5 children can be made happy. The second sample case is an example in which it is impossible to make all C = 7 children happy.

Warning: large input/output data,be careful with certain languages

Added by:	[Trichromatic] XilinX
Date:	2007-05-14
Time limit:	17s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Asia-Pacific Informatics Olympiad(APIO) 2007

SPOJ Problem Set (classical)

1557. Can you answer these queries II

Problem code: GSS2

Being a completist and a simplist, kid Yang Zhe cannot solve but get Wrong Answer from most of the OI problems. And he refuse to write two program of same kind at all. So he always failes in contests.

When having a contest, Yang Zhe looks at the score of every problems first. For the problems of the same score, Yang Zhe will do only one of them. If he's lucky enough, he can get all the scores wanted.

Amber is going to hold a contest in SPOJ. She has made a list of N candidate problems, which fit Yang Zhe very well. So Yang Zhe can solve any problem he want. Amber lined up the problems, began to select. She will select a subsequence of the list as the final problems. Being A girl of great compassion, she'd like to select such a subsequence (can be empty) that Yang Zhe will get the maximal score over all the possible subsequences.

Amber found the subsequence easily after a few minutes. To make things harder, Amber decided that, Yang Zhe can take this contest only if Yang Zhe can answer her Q questions. The question is: if the final problems are limited to be a subsequence of list[X..Y] (1 <= X <= Y <= N), what's the maximal possible score Yang Zhe can get?

As we know, Yang Zhe is a bit idiot (so why did he solve the problem with a negative score?), he got Wrong Answer again... Tell him the correct answer!

Input

Line 1: integer N (1 <= N <= 100000);
Line 2: N integers denoting the score of each problem, each of them is a integer in range [-100000, 100000];
Line 3: integer Q (1 <= Q <= 100000);
Line 3+i (1 <= i <= Q): two integers X and Y denoting the ith question.

Output

Line i: a single integer, the answer to the ith question.

Example

Input:
9
4 -2 -2 3 -1 -4 2 2 -6
3
1 2
1 5
4 9

Output:
4
5
3

Warning: large input/output data,be careful with certain languages

Added by:	[Trichromatic] XilinX
Date:	2007-05-16
Time limit:	1s-5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Description, standard program and test data by Yang Zhe

SPOJ Problem Set (classical)

1644. Trees

Problem code: TREEOI14

Byteasar has a cottage. Lately, he has bought n trees and had them planted all in one row. Byteasar does not, however, like the order which the trees have been planted in. It particularly annoys him that tall and short ones have been mixed up, and the composition does not meet his aesthetic criteria.

Byteasar has invented a disorder coefficient so as to allow the gardener to comprehend his intentions: the lower the value of the coefficient the prettier the row of trees. It is defined in the following way: |h₁−h₂|+ |h₂−h₃|+...+|h_n−1−h_n|, where h₁,h₂, . . . ,h_n are the heights of consecutive trees in a row.

Replanting is a very toilsome and cumbersome task, therefore Byteasar has ordered the gardener to replant two trees at the most (i.e. interchange their positions). The task of the gardener is to choose the pair to replant in a way that makes the disorder coefficient the smallest.

The gardener is not sure if he has chosen the correct pair of trees and he fears he may lose his job if he is mistaken. Help him: for each tree calculate the minimal disorder coefficient that may be attained by switching places with any other tree.

Task

Write a program which:

reads the height of the consecutive trees in a row from the standard input,
for each tree calculates the minimal disorder coefficient that may be attained should it switch places with some other tree (or should there be no change at all),
writes the outcome to the standard output.

Input

The first line of the standard input contains one integer n (2 <= n <= 50000). The other contains n integers h_i (1 <= h_i <= 100000000) separated by single spaces, denoting the height of the consecutive trees in the row.

Output

The output should consist of precisely n lines. The i-th line should contain a single integer - the smallest disorder coefficient attainable when considering replanting of the i-th tree.

Example

Input:
5
7 4 5 2 5

Output:
7
7
8
7
7

* Added some unofficial tests

Added by:	Thanh-Vy Hua
Date:	2007-06-09
Time limit:	1s-6s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Polish Olympiad 14

SPOJ Problem Set ()

1671. Another Mathematical Problem

Problem code: AMATH

Given two numbers n (1<=n<10¹⁰⁰) and k (1<=k<=100), you are to determine whether there exists a positive integer T which satisfies that for every positive integer a, n^a+T-n^a is divisible by 10^k.

Input

Multiple test cases. Each test case contains two space-separated integers n and k. Input terminate by EOF.

The number of test cases will not more than 20.

Output

For each test case, you should output the smallest positive integer number T which satisfies the condition above, or -1 if it doesn't exist.

Example

Input:
32 2

Output:
4

Added by:	[Trichromatic] XilinX
Date:	2007-07-01
Time limit:	3s
Source limit:	2048B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 C99 strict CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	Folklore, description and standard program by Blue Mary

SPOJ Problem Set (classical)

1672. The Great Indian Wedding

Problem code: GIWED

A wedding is to be organized in a rectangular park of dimensions M by N. Some parts of the park are covered by K rectangular carpets. These carpets, produced by ItSucks Corporation are revolutionary self cleaning carpets - they suck any liquid they come in contact with! The organizer wants to water the park to keep the grass fresh. If there were no carpets, the organizer could have used a single pipe to water the whole park but unforunately, the water doesn't seep through the carpets. The organizer has at his diposal L pipes. The pipes would be placed at fixed locations chosen by the organizer and can't be moved. Water spreads from a pipe in all directions unless obstructed by the park boundary or a carpet. What is the maximum area that can be watered using these L pipes?

Input

The first line of the input contains a single integer T, the number of test cases (1<=T<=30) . Each test case starts with a single line containg the values M,N,K and L ( 1<=M<=10000, 1<=N<=10000, 0<=K<=50, 1<=L<=10). It is followed by K lines, each line containing 4 integers separated by single spaces, x₁,y₁,x₂,y₂where (x₁,y₁) and (x₂,y₂) are the zero based coordinates of lower left and upper right vertex of the carpet. Assume that x₁<x₂and y₁<y₂. The carpets may cover each other. Water would not be able to seep through even if two carpets touch in a corner.

Output

For each test case, print the maximum area that can be watered on a single line

Example

Input:
2
10 10 0 1
10 10 1 1
3 3 4 4

Output:
100
99

Added by:	Rahul Garg
Date:	2007-07-04
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	C-maphore, Tryst 2007

SPOJ Problem Set (classical)

1673. Ambitious Manager

Problem code: AMBM

The Bogus Corporation distributes salary to its employees in a weird manner. The salary is distributed every K days, and instead of same salary for each day, the salary for the i^th day is a_i. An ambitious young manager, fresh from Institute of Mismanagement, observes that people usually prefer to take leave towards the end of this period of K days, when the workload is higher. Instead of revising each of the a_i's, the manager comes up with a quick fix solution - he redefines the new salary on the i^th day as b_i=a_i+2a_i-1+2²a_i-2+2³a_i-3+........+2^i-1a₁ . Baba, one of the employees, is in a dire financial crisis, and must accumulate at least N rupees at the end of the forthcoming period. Being a lazy worker that he is, he is interested in finding out if attending particular days would guarantee him exactly N rupees at the end of the period. Can you help Baba?

Input

First line contains a single integer integer T, the number of test cases ( 1<=T<=100). Each test case is described on two lines. First line contains two integers, N and K ( 1<=N<=2⁶³-1, 1<=K<=50) , the second line contains a space separated list of K integers, the a_i's ( 1<=a_i<=1000).

Output

For each test case, output on a single line 1-based indices of the days (separated by a single space) he should attend to ensure a salary of exactly N rupees at the end of the period. The indices should be printed in the sorted order. In case of multiple answers, output any one of them. If there is no answer, print -1.

Example

Input:
2
9 3
1 1 2
10 2
2 3
Output:
1 3
-1

Added by:	Rahul Garg
Date:	2007-07-04
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	C-maphore, Tryst 2007

SPOJ Problem Set (classical)

1674. The Explosion

Problem code: EXPLOSN

The day of 6.XII.2003 in Megabyteland began calm and quietly as any other day. Some people went to work, some - to school, some - to store to buy food. Drivers were traditionally stucked in traffic jams, drinking coffee and reading morning newspaper. Suddenly the regularity of this day was disturbed by huge explosion."They blew up the embassy of Bajtocja!!!" - somebody cried. Everybody began to run away in panic.

Police works pretty good in Megabyteland and first radiocars appeared near the embassy only few seconds after the explosion. All the people near the embassy were detained. Some of these people are the organizers of the explosion, but the others could by just occasional witnesses. During the testification each person named exactly one perpetrator. It is known, that if a man is not a perpetrator, than he always says the truth (he haven't a reason to lie, have he?). However, perpetrators want to make the work of the police more difficult, so a perpetrator can name any person during the testification (even himself).

The policemen are in the very hard situation. They should arrest some group of potential perpetrators, but it is difficult to determine who is guilty and who is not from the data they have. There exists many groups of potential perpetrators, that don't contradict to any of the testimonies. The policemen want to arrest as small innocent people as possible. So they would like to choose the group with minimal number of people.

Write a program that, given the number of detained people and their testimonies, will determine the number of people in the smallest group of potential perpetrators, that don't contradict to the testimonies.

Input

The first line of the input contains a single integer T, the number of testcases (1<=T<=10).

First line of each testcase contains integer number N (2 <= N <= 100000), equal to the number of detained people (the people are numbered from 1 to N). The i-th of the following N lines contain one integer number Pi (1 <= Pi <= N). Here Pi is the man whom i-th man testified to be guilty.

Output

The output should consist of T lines, containing one integer number for each testcase - the number of people in the smallest group of potential perpetrators, that don't contradict to the testimonies.

Example

Input:
1
3
2
3
1

Output:
2

Added by:	Bin Jin
Date:	2007-07-04
Time limit:	1s-2s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C++ 4.0.0-8
Resource:	First Minsk Training Camp for NEERC teams, day 2 – MWPZ' 2003

SPOJ Problem Set (classical)

1675. Fusion Cube

Problem code: FUSION

The Bogus Corporation claims to have solved the energy crisis by devising a method to perform controlled fusion reaction! The set up consists of a cube of side length N meters, which contain K point sources of electrons. Each of the sources can be configured to emanate an electron along any of the six possible directions corresponding to +X axis, -X axis, +Y axis, -Y axis, +Z axis, -Z axis. The cube is filled with a medium in which the electrons travel with a velocity of 1m/s. At time t=0, all the sources are switched on simultaneously, emanating a single electron along the configured direction. An electron travels in a straight line until it strikes the boundary of the cube or collides with another electron. A collision between two electrons can occur in two possible ways - a head-on collision, and a side-on collision. In a head-on collision, both the electrons rebound in opposite directions with the same speed. A side-on collision occurs when the colliding electrons are travelling in mutually perpendicular directions. After a side-on collision, the colliding electrons are deflected by 90 degrees, rebounding in mutually perpendicular directions with the same speed, the plane of motion remaining the same. Note that throughout the experiment, the direction of motion of an electron remains oriented along one of the coordinate axes. If more than two electrons collide simultaneously, resolve the collision pairwise, where any two of the colliding electrons can be paired. To maximize the chances of initiating the fusion reaction, we would like to maximize the time before an electron hits a boundary wall of the cube. Given the location of the K sources, determine the orientation of the sources such that this time is maximized. Output this maximum value.

Input

First line contains a single integer T, the number of test cases ( 1<=T<=50), followed by the description of the test cases. The first line of each test case contains two integers, K and N respectively ( 1<=K<=100, 1<=N<=1000). It is followed by K lines, where each line contains space separated three integers representing the X, Y and Z coordinates of the particular source. The coordinates of the diagonally opposite corners of the cube are (0,0,0) and (N,N,N). All the sources will lie strictly inside the cube.

Output

For each test case, output the maximum value of the time before the first electron hits the boundary of the cube on a single line.

Example

Input:
2
1 10
5 5 5
2 10
1 1 1
1 1 2
Output:
5
9

Added by:	Rahul Garg
Date:	2007-07-04
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	C-maphore, Tryst 2007

SPOJ Problem Set (classical)

1676. Text Generator

Problem code: GEN

LoadingTime has been given a task these days. He is required to write a tool called Text Generator. This software is widely used among the kids who are under seven. It generates an article with the size of a given number L for users. If an article contains at least one word which the users know, we consider it readable. Now, LoadingTime wants to know, how many readable articles can it generates, and he can improve his Text Generator. Could you help him??

Input

The input contains multiple test cases.

The first line of each test case contains two integer N (1 <= N <= 10), L (1 <= L <= 1000000). The following N lines contain N words representing the words knew by the users. All the words and the generated article only contain uppercase letters, and the length of each word is not greater than 6.

Output

For each test case, your program should output a integer as LoadingTime required. As the number could be quite large, you only need to print the answer modulo 10007.

Example

Input:
2 2
A
B
2 10000
ABC
B

Output:
100
5960

Added by:	Bin Jin
Date:	2007-07-05
Time limit:	10s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C++ 4.0.0-8
Resource:

SPOJ Problem Set (classical)

1677. Halloween treats

Problem code: HALLOW

Every year there is the same problem at Halloween: Each neighbor is only willing to give a certain total number of sweets on that day, no matter how many children call on him, so it may happen that a child will get nothing if it is too late. To avoid conflicts, the children have decided they will put all sweets together and then divide them evenly among themselves. From last year's experience of Halloween they know how many sweets they get from each neighbour. Since they care more about justice than about the number of sweets they get, they want to select a subset of the neighbours to visit, so that in sharing every child receives the same number of sweets. They will not be satisfied if they have any sweets left which cannot be divided.

Your job is to help the children and present a solution.

Input

The input contains several test cases.
The first line of each test case contains two integers c and n (1 ≤ c ≤ n ≤ 100000), the number of children and the number of neighbours, respectively. The next line contains n space separated integers a₁ , ... , a_n (1 ≤ a_i ≤ 100000 ), where a_i represents the number of sweets the children get if they visit neighbour i.

The last test case is followed by two zeros.

Output

For each test case output one line with the indices of the neighbours the children should select (here, index i corresponds to neighbour i who gives a total number of a_i sweets). If there is no solution where each child gets at least one sweet, print "no sweets" instead. Note that if there are several solutions where each child gets at least one sweet, you may print any of them.

Example

Input:
4 5
1 2 3 7 5
3 6
7 11 2 5 13 17
0 0


Output:
3 5
2 3 4

Added by:	Simon Gog
Date:	2007-07-05
Time limit:	15s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	University of Ulm Local Contest 2007/2008

SPOJ Problem Set (classical)

1678. Royal Treasury

Problem code: TREASURY

Once upon a time in a kingdom far far away, the royal treasury started getting emptier and emptier. The king decided to change the situation and he invented a new system of cooperation with in the office of the royal treasurer. The clerks of the office are supposed to form pairs (in order to avoid being bribed) in such away that each pair is formed by a clerk and his/her direct subordinate. Your task is to compute, given the structure of the office of the treasurer, the maximum number of pairs that can be formed this way and in how many different ways this is possible.

The office of the treasurer is led by George Skinflint. Each clerk has zero, one or more subordinates and is a subordinate of a single clerk (except for George Skinflint who is responsible only to the king himself). The number of clerks does not exceed 1000. Your task is to compute the maximum number of pairs that can be formed by clerks in such a way that every pair is formed by a clerk and his/her direct subordinate. In addition, you should also compute the number of ways such pairs can be formed. Note that some clerks need not be contained in a pair.

Input

The input contains multiple testcases.

The first line of each testcase contains a single number N that represents the number of clerks 1 <= N <= 1000. The clerks are assigned unique ID numbers from the range between 1 and N. The ID number of the treasurer (Skinflint) is 1. Each of the following N lines corresponds to one of the clerks: it contains his/her ID number, the number K of his/her subordinates, 0 <= K <= 999, and the ID numbers of his/her K subordinates separated by single spaces. You can assume that the line corresponding to a clerk never appears before the line corresponding to his/her supervisor.

Output

The output for each testcase should consist of two lines. The first line of the output should contain a single number that represents the maximum number M of pairs that the clerks can form. The second line should contain the number of different ways in which the clerks can form M pairs obeying the rules given by the king.

Example

Input:
7
1 3 2 4 7
2 1 3
4 1 6
3 0
7 1 5
5 0
6 0

Output:
3
4

Added by:	Bin Jin
Date:	2007-07-06
Time limit:	0.5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C++ 4.0.0-8
Resource:	CEOI 2007, day 2

SPOJ Problem Set (classical)

1681. Cylinder

Problem code: CYLINDER

Using a sheet of paper and scissors, you can cut out two faces to form a cylinder in the following way:

Cut the paper horizontally (parallel to the shorter side) to get two rectangular parts.
From the first part, cut out a circle of maximum radius. The circle will form the bottom of the cylinder.
Roll the second part up in such a way that it has a perimeter of equal length with the circle's circumference, and attach one end of the roll to the circle. Note that the roll may have some overlapping parts in order to get the required length of the perimeter.

Given the dimensions of the sheet of paper, can you calculate the biggest possible volume of a cylinder which can be constructed using the procedure described above?

Input Specification

The input consists of several test cases. Each test case consists of two numbers w and h (1 ≤ w ≤ h ≤ 100), which indicate the width and height of the sheet of paper.

The last test case is followed by a line containing two zeros.

Output Specification

For each test case, print one line with the biggest possible volume of the cylinder. Round this number to 3 places after the decimal point.

Sample Input

Sample Output

54.247
785.398
412.095

In the first case, the optimal cylinder has a radius of about 1.591549, in the second case, the optimal cylinder has a radius of 5, and in the third case, the optimal cylinder has a radius of about 3.621795.

Added by:	Adrian Kuegel
Date:	2007-07-06
Time limit:	4s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	own problem, used in University of Ulm Local Contest 2007

SPOJ Problem Set (classical)

1683. Expressions

Problem code: EXPRESS

Arithmetic expressions are usually written with the operators in between the two operands (which is called infix notation). For example, (x+y)*(z-w) is an arithmetic expression in infix notation. However, it is easier to write a program to evaluate an expression if the expression is written in postfix notation (also known as reverse polish notation). In postfix notation, an operator is written behind its two operands, which may be expressions themselves. For example, x y + z w - * is a postfix notation of the arithmetic expression given above. Note that in this case parentheses are not required.

To evaluate an expression written in postfix notation, an algorithm operating on a stack can be used. A stack is a data structure which supports two operations:

push: a number is inserted at the top of the stack.
pop: the number from the top of the stack is taken out.

During the evaluation, we process the expression from left to right. If we encounter a number, we push it onto the stack. If we encounter an operator, we pop the first two numbers from the stack, apply the operator on them, and push the result back onto the stack. More specifically, the following pseudocode shows how to handle the case when we encounter an operator O:

a := pop();
b := pop();
push(b O a);

The result of the expression will be left as the only number on the stack.

Now imagine that we use a queue instead of the stack. A queue also has a push and pop operation, but their meaning is different:

push: a number is inserted at the end of the queue.
pop: the number from the front of the queue is taken out of the queue.

Can you rewrite the given expression such that the result of the algorithm using the queue is the same as the result of the original expression evaluated using the algorithm with the stack?

Input Specification

The first line of the input contains a number T (T ≤ 200). The following T lines each contain one expression in postfix notation. Arithmetic operators are represented by uppercase letters, numbers are represented by lowercase letters. You may assume that the length of each expression is less than 10000 characters.

Output Specification

For each given expression, print the expression with the equivalent result when using the algorithm with the queue instead of the stack. To make the solution unique, you are not allowed to assume that the operators are associative or commutative.

Sample Input

2
xyPzwIM
abcABdefgCDEF

Sample Output

wzyxIPM
gfCecbDdAaEBF

Added by:	Adrian Kuegel
Date:	2007-07-06
Time limit:	4s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	own problem, used in University of Ulm Local Contest 2007

SPOJ Problem Set (classical)

1684. Frequent values

Problem code: FREQUENT

You are given a sequence of n integers a₁ , a₂ , ... , a_n in non-decreasing order. In addition to that, you are given several queries consisting of indices i and j (1 ≤ i ≤ j ≤ n). For each query, determine the most frequent value among the integers a_i , ... , a_j.

Input Specification

The input consists of several test cases. Each test case starts with a line containing two integers n and q (1 ≤ n, q ≤ 100000). The next line contains n integers a₁ , ... , a_n (-100000 ≤ a_i ≤ 100000, for each i ∈ {1, ..., n}) separated by spaces. You can assume that for each i ∈ {1, ..., n-1}: a_i ≤ a_i+1. The following q lines contain one query each, consisting of two integers i and j (1 ≤ i ≤ j ≤ n), which indicate the boundary indices for the query.

The last test case is followed by a line containing a single 0.

Output Specification

For each query, print one line with one integer: The number of occurrences of the most frequent value within the given range.

Sample Input

10 3
-1 -1 1 1 1 1 3 10 10 10
2 3
1 10
5 10
0

Sample Output

1
4
3

A naive algorithm may not run in time!

Added by:	Adrian Kuegel
Date:	2007-07-06
Time limit:	5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	University of Ulm Local Contest 2007

SPOJ Problem Set (classical)

1685. Grocery store

Problem code: GROCERY

A cashier in a grocery store seems to have difficulty in distinguishing the multiplication symbol and the addition symbol. To make things easier for him, you want to buy goods in such a way that the product of their prices is the same as the sum of their prices.

Of course, if you buy only one item, this is always true. With two items and three items, it still seems quite a boring task to you, so now you are interested in finding possible prices of four items such that the sum of the four prices is equal to the product of the four prices. You should consider the prices are in € with two digits after the decimal point. Obviously, each product costs at least one cent.

Input Specification

This problem has no input.

Output Specification

Print all solutions which have a sum of the four items of at most 20.00 €. For each solution, print one line with the prices of the four items in non-decreasing order, with one space character between them. You may print the solutions in any order, but make sure to print each solution only once.

Sample Output

0.50 1.00 2.50 16.00
1.25 1.60 1.75 1.84
1.25 1.40 1.86 2.00
...

Added by:	Adrian Kuegel
Date:	2007-07-06
Time limit:	1.600s
Source limit:	600B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	University of Ulm Local Contest 2007

SPOJ Problem Set (classical)

1687. Logic II

Problem code: LOGIC2

Some day in 2003 in Byteland began calm and quietly as any other day. Some people went to work, some to school, some to store to buy food. Drivers were traditionally stucked in traffic jams, drinking coffee and reading morning newspaper. Suddenly the regularity of this day was disturbed by huge explosion."They blew up the embassy of Bajtocja!!!" somebody cried. Everybody began to run away in panic.

Police works pretty good in Byteland and first radiocars appeared near the embassy only few seconds after the explosion. All the people near the embassy were detained. Only one of the people is the organizer of the explosion, the others could by just occasional witnesses. It is known, among these M(1<=M<=11) people, N(1<=N<=M) people always lie because they want to make the work of police more difficult, the others always tell the truth.

All these people say P(1<=P<=30) sentences in total.All the useful sentences are in one of the 4 forms below, all the other sentences are useless and you can ignore them.

I am guilty.
I am not guilty.
Somebody is guilty.
Somebody is not guilty.
Today is Someday.

Among these sentences, Somebody is a name of one of these M people, and Someday is Monday, Tuesday, Wednesday, Thursday, Friday, Saturday or Sunday.

Your task is to help the police to find out the only one organizer of the explosion.

Input

Multiple test cases. For each test case:

The first line contains three integers M, N and P. M lines follow, each contains a name of one of the people.All names contain only capital Latin letters and no whitespaces.P lines come next, each contains no more than 250 characters, the speaker and his/her speech. See the example.

You can assume that there's no whitespace at the start and the end of a line, and there are no two consecutive spaces in the input.

Input terminate by EOF.

Output

The name of the organizer if you can determine, or Cannot Determine if you find more than one, or Impossible if you find no one.

Example

Input:
3 1 5
MIKE
CHARLES
KATE
MIKE: I am guilty.
MIKE: Today is Sunday.
CHARLES: MIKE is guilty.
KATE: I am guilty.
KATE: How are you??

Output:
MIKE

Added by:	[Trichromatic] XilinX
Date:	2007-07-13
Time limit:	13s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Description by Blue Mary

SPOJ Problem Set (classical)

1688. A Very Easy Problem!

Problem code: EASYPROB

Input

There's no input.

Output

Output some form of these numbers: 137, 1315, 73, 136, 255, 1384, 16385, one per line in the listed order.

Example

The first two lines of the CORRECT output file are:

137=2(2(2)+2+2(0))+2(2+2(0))+2(0)
1315=2(2(2+2(0))+2)+2(2(2+2(0)))+2(2(2)+2(0))+2+2(0)

The correct output file should contain 7 lines.

Added by:	[Trichromatic] XilinX
Date:	2007-07-13
Time limit:	1s
Source limit:	500B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	TEXT
Resource:	You can imagine it.

SPOJ Problem Set (classical)

1689. Hard Problem

Problem code: HARDP

[This space is intentionally left blank.]

Input

Multiple test cases. Each contains a single integer N(1<=N<=50). Input terminates by EOF.

Output

For each test case, output one line contains the answer. See the example.

Example

Input:
8
9
10

Output:
8=90*(0+0+0+0+45-3+20-42+60+10)
9=20*(0-3+10-14+15+2+0+0+0+0+10)
10=66*(0+0+0+0+0+33+5-33+66-66+55+6)

Added by:	[Trichromatic] XilinX
Date:	2007-07-14
Time limit:	11s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Based on a problem from an ACM/ICPC Regional Contest

SPOJ Problem Set (classical)

1693. Coconuts

Problem code: COCONUTS

A group of n castle guards are voting to determine whether African swallows can carry coconuts. While each guard has his own personal opinion on the matter, a guard will often vote contrary to his beliefs in order to avoid disagreeing with the votes of his friends.
You are given a list of guards who either do or do not believe in the coconut-carrying capacity of African swallows, and a list of all pairs of guards who are friends. Your task is to determine how each guard must vote in order to minimize the sum of the total number of disagreements between friends and the total number of guards who must vote against their own beliefs.

Input

The input to this problem will contain multiple test cases. Each test case begins with a single line containing an integer n (where 2 <= n <= 300), the number of guards, and an integer m (where 1 <= m <= n(n-1)/2), the number of pairs of guards who are friends. The second line of the test case contains n integers, where the ith integer is 1 if the ith guard believes in the ability of African swallows to carry coconuts, and 0 otherwise. Finally, the next m lines of the test case each contain two distinct integers i and j (where 1 <= i, j <= n), indicating that guards i and j are friends. Guards within each pair of friends may be listed in any order, but no pair of guards will be repeated. The input is terminated by an invalid test case with n = m = 0, which should not be processed.

Output

For each input test case, print a single line containing the minimum possible sum of the total number of disagreements between all friends plus the total number of guards who must vote against their own beliefs.

Example

Input:
3 3
1 0 0
1 2
1 3
3 2
6 6
1 1 1 0 0 0
1 2
2 3
4 2
3 5
4 5
5 6
0 0

Output:
1
2

Added by:	Bin Jin
Date:	2007-07-22
Time limit:	1s
Source limit:	5000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C++ 4.0.0-8
Resource:	Pacific NW 2006

SPOJ Problem Set (classical)

1695. Grandpa’s Rubik Cube

Problem code: GRC

Documento sin título

A very well-known toy/pastime, called Rubik's cube, consists of a cube as shown in Figure 1a, where letters stand for colors (e.g. B for blue, R for red,...). The goal of the game is to rotate the faces of the cube in such a way that at the end each face has a different color, as shown in Figure 1b. Notice that,

when a face is rotated, the configuration of colors in all the adjacent faces changes. Figure 2 illustrates a rotation of one of the faces. Given a scrambled configuration, reaching the final position can be quite challenging, as you may know.

But your grandpa has many years of experience, and claims that, given any configuration of the Rubik cube, he can come up with a sequence of rotations leading to a winning configuration. In order to show all faces of the cube we shall represent the cube as in Figure 3a. The six colors are Yellow, Red, Blue, Green, White and Magenta (represented by their first letters).
You will be given an initial configuration and a list of rotations. A rotation will be represented by an integer number, indicating the face to be rotated and the direction of the rotation (a positive value means clockwise rotation, negative value means counter-clockwise rotation). Faces of the cube are numbered as shown in Figure 3b. You must write a program that checks whether the list of rotations will lead to a winning configuration.

Input
The input contains several test cases. The first line of the input is an integer which indicates the number of tests. Each test description consists of ten lines of input. The first nine lines of a test will describe an initial configuration, in the format shown in Figure 3a. The next line will contain a list of rotations, ending with the value 0.

Output
For each test case your program should print one line. If your grandpa is correct, print “Yes, grandpa!”, otherwise print “No, you are wrong!”. (See example.)

Added by:	Andrés Leonardo Rojas Duarte
Date:	2007-07-24
Time limit:	5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS
Resource:	ACM International Collegiate Programming Contest 2002 – South America

SPOJ Problem Set (classical)

1696. Will Indiana Jones Get There

Problem code: WIJGT

Documento sin título

Indiana Jones is in a deserted city, annihilated during a war. Roofs of all houses have been destroyed and only portions of walls are still standing. The ground is so full of mines that the only safe way to move around the city is walking over the remaining walls. The mission of our hero is to save a person who is trapped in the city. In order to move between two walls which are not connected Indiana Jones thought of taking with him a wooden board which he could place between the two walls and then cross from one to the other.

Initial positions of Indiana Jones and the trapped person are both on some section of the walls. Besides, walls are either in the direction South-North or West-East. You will be given a map of the city remains. Your mission is to determine the minimum length of the wooden board Indiana Jones needs to carry in order to get to the trapped person.

Input
Your program should process several test cases. Each test case starts with an integer N indicating the number of wall sections remaining in the city (2 <= N <= 1000). Each of the next N lines describes a wall section. The first wall section to appear is the section where Indiana Jones stands at the beginning. The second section to appear is the section where the trapped person stands. Each wall section description consists of three integers X , Y and L (–10000 <= X , Y , L <= 10000), where X an Y define either the southernmost point of a wall section (for South-North sections) or the westernmost point
(for West-East wall sections). The value of L determines the length and direction of the wall: if L > 0, the section is West-East, with length L ; if L< 0, the section is North-South, with length | L | . The end of input is indicated by N = 0.

Output
For each test case in the input your program should produce one line of output, containing a real value representing the length of the wooden board Indiana Jones must carry. The length must be printed as a real number with two-digit precision, and the last decimal digit must be rounded. The input will not contain test cases where differences in rounding are significant.

Sample input
14
1 1 5
6 8 2
7 2 -2
5 3 3
2 5 2
2 3 2
2 3 -2
4 3 -2
0 7 1
1 8 2
3 6 -2
4 7 2
6 6 1
6 6 -2
3
-10 0 20
-5 1 10
50 50 100
0

Output for the sample input
1.41
1.00

Added by:	Andrés Leonardo Rojas Duarte
Date:	2007-07-25
Time limit:	10s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS
Resource:	ACM International Collegiate Programming Contest 2002 – South America

SPOJ Problem Set ()

1697. Ohgas' Fortune

Problem code: OFORTUNE

The Ohgas are a prestigious family based on Hachioji. The head of the family, Mr. Nemochi Ohga, a famous wealthy man, wishes to increase his fortune by depositing his money to an operation company. You are asked to help Mr. Ohga maximize his profit by operating the given money during a specified period.

From a given list of possible operations, you choose an operation to deposit the given fund to. You commit on the single operation throughout the period and deposit all the fund to it. Each operation specifies an annual interest rate, whether the interest is simple or compound, and an annual operation charge. An annual operation charge is a constant not depending on the balance of the fund. The amount of interest is calculated at the end of every year, by multiplying the balance of the fund under operation by the annual interest rate, and then rounding off its fractional part. For compound interest, it is added to the balance of the fund under operation, and thus becomes a subject of interest for the following years. For simple interest, on the other hand, it is saved somewhere else and does not enter the balance of the fund under operation (i.e. it is not a subject of interest in the following years). An operation charge is then subtracted from the balance of the fund under operation. You may assume here that you can always pay the operation charge (i.e. the balance of the fund under operation is never less than the operation charge). The amount of money you obtain after the specified years of operation is called ``the final amount of fund.'' For simple interest, it is the sum of the balance of the fund under operation at the end of the final year, plus the amount of interest accumulated throughout the period. For compound interest, it is simply the balance of the fund under operation at the end of the final year.

Operation companies use C, C++, Java, etc., to perform their calculations, so they pay a special attention to their interest rates. That is, in these companies, an interest rate is always an integral multiple of 0.0001220703125 and between 0.0001220703125 and 0.125 (inclusive). 0.0001220703125 is a decimal representation of 1/8192. Thus, interest rates' being its multiples means that they can be represented with no errors under the double-precision binary representation of floating-point numbers.

For example, if you operate 1000000 JPY for five years with an annual, compound interest rate of 0.03125 (3.125 %) and an annual operation charge of 3000 JPY, the balance changes as follows.
The balance of the fund under operation(at the beginning of year) Interest The balance of the fund under operation (at the end of year)
A B = A × 0.03125 (and rounding off fractions) A + B - 3000
1000000 31250 1028250
1028250 32132 1057382
1057382 33043 1087425
1087425 33982 1118407
1118407 34950 1150357

After the five years of operation, the final amount of fund is 1150357 JPY.

If the interest is simple with all other parameters being equal, it looks like:
The balance of the fund under operation (at the beginning of year) Interest The balance of the fund under operation (at the end of year) Cumulative interest
A B = A × 0.03125 (and rounding off fractions) A - 3000
1000000 31250 997000 31250
997000 31156 994000 62406
994000 31062 991000 93468
991000 30968 988000 124436
988000 30875 985000 155311

In this case the final amount of fund is the total of the fund under operation, 985000 JPY, and the cumulative interests, 155311 JPY, which is 1140311 JPY.

Input

The input consists of datasets. The entire input looks like:

The number of datasets, m, is no more than 100. Each dataset is formatted as follows.

The initial amount of the fund for operation, the number of years of operation, and the number of available operations are all positive integers. The first is no more than 100000000, the second no more than 10, and the third no more than 100.

Each ``operation'' is formatted as follows.

simple-or-compound annual-interest-rate annual-operation-charge
where simple-or-compound is a single character of either '0' or '1', with '0' indicating simple interest and '1' compound. annual-interest-rate is represented by a decimal fraction and is an integral multiple of 1/8192. annual-operation-charge is an integer not exceeding 100000.

Output

For each dataset, print a line having a decimal integer indicating the final amount of fund for the best operation. The best operation is the one that yields the maximum final amount among the available operations. Each line should not have any character other than this number.

You may assume the final balance never exceeds 1000000000. You may also assume that at least one operation has the final amount of the fund no less than the initial amount of the fund.

Example

Input:
4
1000000
5
2
0 0.03125 3000
1 0.03125 3000
6620000
7
2
0 0.0732421875 42307
1 0.0740966796875 40942
39677000
4
4
0 0.0709228515625 30754
1 0.00634765625 26165
0 0.03662109375 79468
0 0.0679931640625 10932
10585000
6
4
1 0.0054931640625 59759
1 0.12353515625 56464
0 0.0496826171875 98193
0 0.0887451171875 78966

Output:
1150357
10559683
50796918
20829397

Added by:	Camilo Andrés Varela León
Date:	2007-07-26
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 n SCALA SED TCL
Resource:	Japan Domestic, 2005

SPOJ Problem Set ()

1698. Polygonal Line Search

Problem code: PLSEARCH

Multiple polygonal lines are given on the xy-plane. Given a list of polygonal lines and a template, you must find out polygonal lines which have the same shape as the template.

A polygonal line consists of several line segments parallel to x-axis or y-axis. It is defined by a list of xy-coordinates of vertices from the start-point to the end-point in order, and always turns 90 degrees at each vertex. A single polygonal line does not pass the same point twice. Two polygonal lines have the same shape when they fully overlap each other only with rotation and translation within xy-plane (i.e. without magnification or a flip). The vertices given in reverse order from the start-point to the end-point is the same as that given in order.

Figure 1 shows examples of polygonal lines. In this figure, polygonal lines A and B have the same shape.

Write a program that answers polygonal lines which have the same shape as the template.

Figure 1: Polygonal lines

Input

The input consists of multiple datasets. The end of the input is indicated by a line which contains a zero.

A dataset is given as follows.

n
Polygonal line0
Polygonal line1
Polygonal line2
...
Polygonal linen

n is the number of polygonal lines for the object of search on xy-plane. n is an integer, and 1 <= n <= 50. Polygonal line0 indicates the template.

A polygonal line is given as follows.

m
x1 y1
x2 y2
...
xm ym

m is the number of the vertices of a polygonal line (3 <= m <= 10). xi and yi, separated by a space, are the x- and y-coordinates of a vertex, respectively (-10000 < xi < 10000, -10000

Output

For each dataset in the input, your program should report numbers assigned to the polygonal lines that have the same shape as the template, in ascending order. Each number must be written in a separate line without any other characters such as leading or trailing spaces.

Five continuous "+"s must be placed in a line at the end of each dataset.

Example

Added by:	Camilo Andrés Varela León
Date:	2007-07-26
Time limit:	3s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Japan Domestic, 2005

SPOJ Problem Set (classical)

1699. Numeral System

Problem code: NSYSTEM

Prof. Hachioji has devised a new numeral system of integral numbers with four lowercase letters "m", "c", "x", "i" and with eight digits "2", "3", "4", "5", "6", "7", "8", "9". He doesn't use digit "0" nor digit "1" in this system.

The letters "m", "c", "x" and "i" correspond to 1000, 100, 10 and 1, respectively, and the digits "2", ...,"9" correspond to 2, ..., 9, respectively. This system has nothing to do with the Roman numeral system.

For example, character strings

"5m2c3x4i", "m2c4i" and "5m2c3x"

correspond to the integral numbers 5234 (=5*1000+2*100+3*10+4*1), 1204 (=1000+2*100+4*1), and 5230 (=5*1000+2*100+3*10), respectively. The parts of strings in the above example, "5m", "2c", "3x" and "4i" represent 5000 (=5*1000), 200 (=2*100), 30 (=3*10) and 4 (=4*1), respectively.

Each of the letters "m", "c", "x" and "i" may be prefixed by one of the digits "2", "3", ..., "9". In that case, the prefix digit and the letter are regarded as a pair. A pair that consists of a prefix digit and a letter corresponds to an integer that is equal to the original value of the letter multiplied by the value of the prefix digit.

For each letter "m", "c", "x" and "i", the number of its occurrence in a string is at most one. When it has a prefix digit, it should appear together with the prefix digit. The letters "m", "c", "x" and "i" must appear in this order, from left to right. Moreover, when a digit exists in a string, it should appear as the prefix digit of the following letter. Each letter may be omitted in a string, but the whole string must not be empty. A string made in this manner is called an MCXI-string.

An MCXI-string corresponds to a positive integer that is the sum of the values of the letters and those of the pairs contained in it as mentioned above. The positive integer corresponding to an MCXI-string is called its MCXI-value. Moreover, given an integer from 1 to 9999, there is a unique MCXI-string whose MCXI-value is equal to the given integer. For example, the MCXI-value of an MCXI-string "m2c4i" is 1204 that is equal to 1000 + 2*100 + 4*1. There are no MCXI-strings but "m2c4i" that correspond to 1204. Note that strings "1m2c4i", "mcc4i", "m2c0x4i", and "2cm4i" are not valid MCXI-strings. The reasons are use of "1", multiple occurrences of "c", use of "0", and the wrong order of "c" and "m", respectively.

Your job is to write a program for Prof. Hachioji that reads two MCXI-strings, computes the sum of their MCXI-values, and prints the MCXI-string corresponding to the result.

Input

The input is as follows. The first line contains a positive integer n (<= 500) that indicates the number of the following lines. The k+1 th line is the specification of the k th computation (k=1, ..., n).

n
specification1
specification2
...
specificationn

Each specification is described in a line:

MCXI-string1 MCXI-string2

The two MCXI-strings are separated by a space.

You may assume that the sum of the two MCXI-values of the two MCXI-strings in each specification is less than or equal to 9999.

Output

For each specification, your program should print an MCXI-string in a line. Its MCXI-value should be the sum of the two MCXI-values of the MCXI-strings in the specification. No other characters should appear in the output.

Example

Input:
10
xi x9i
i 9i
c2x2i 4c8x8i
m2ci 4m7c9x8i
9c9x9i i
i 9m9c9x8i
m i
i m
m9i i
9m8c7xi c2x8i

Output:
3x
x
6cx
5m9c9x9i
m
9m9c9x9i
mi
mi
mx
9m9c9x9i

Added by:	Camilo Andrés Varela León
Date:	2007-07-26
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Japan Domestic, 2005

SPOJ Problem Set (classical)

1700. Traveling by Stagecoach

Problem code: TRSTAGE

Once upon a time, there was a traveler.

He plans to travel using stagecoaches (horse wagons). His starting point and destination are fixed, but he cannot determine his route. Your job in this problem is to write a program which determines the route for him.

There are several cities in the country, and a road network connecting them. If there is a road between two cities, one can travel by a stagecoach from one of them to the other. A coach ticket is needed for a coach ride. The number of horses is specified in each of the tickets. Of course, with more horses, the coach runs faster.

At the starting point, the traveler has a number of coach tickets. By considering these tickets and the information on the road network, you should find the best possible route that takes him to the destination in the shortest time. The usage of coach tickets should be taken into account.

The following conditions are assumed.

A coach ride takes the traveler from one city to another directly connected by a road. In other words, on each arrival to a city, he must change the coach.
Only one ticket can be used for a coach ride between two cities directly connected by a road.
Each ticket can be used only once.
The time needed for a coach ride is the distance between two cities divided by the number of horses.
The time needed for the coach change should be ignored.

Input

The input consists of multiple datasets, each in the following format. The last dataset is followed by a line containing five zeros (separated by a space).

n m p a b
t1 t2 ... tn
x1 y1 z1
x2 y2 z2
...
xp yp zp

Every input item in a dataset is a non-negative integer. If a line contains two or more input items, they are separated by a space.

n is the number of coach tickets. You can assume that the number of tickets is between 1 and 8. m is the number of cities in the network. You can assume that the number of cities is between 2 and 30. p is the number of roads between cities, which may be zero.

a is the city index of the starting city. b is the city index of the destination city. a is not equal to b. You can assume that all city indices in a dataset (including the above two) are between 1 and m.

The second line of a dataset gives the details of coach tickets. ti is the number of horses specified in the i-th coach ticket (1<=i<=n). You can assume that the number of horses is between 1 and 10.

The following p lines give the details of roads between cities. The i-th road connects two cities with city indices xi and yi, and has a distance zi (1<=i<=p). You can assume that the distance is between 1 and 100.

No two roads connect the same pair of cities. A road never connects a city with itself. Each road can be traveled in both directions.

Output

For each dataset in the input, one line should be output as specified below. An output line should not contain extra characters such as spaces.

If the traveler can reach the destination, the time needed for the best route (a route with the shortest time) should be printed. The answer should not have an error greater than 0.001. You may output any number of digits after the decimal point, provided that the above accuracy condition is satisfied.

If the traveler cannot reach the destination, the string "Impossible" should be printed. One cannot reach the destination either when there are no routes leading to the destination, or when the number of tickets is not sufficient. Note that the first letter of "Impossible" is in uppercase, while the other letters are in lowercase.

Example

Input:
3 4 3 1 4
3 1 2
1 2 10
2 3 30
3 4 20
2 4 4 2 1
3 1
2 3 3
1 3 3
4 1 2
4 2 5
2 4 3 4 1
5 5
1 2 10
2 3 10
3 4 10
1 2 0 1 2
1
8 5 10 1 5
2 7 1 8 4 5 6 3
1 2 5
2 3 4
3 4 7
4 5 3
1 3 25
2 4 23
3 5 22
1 4 45
2 5 51
1 5 99
0 0 0 0 0

Output:
30.000
3.667
Impossible
Impossible
2.856

Since the number of digits after the decimal point is
not specified, the above result is not the only
solution. For example, the following result is also acceptable.

30.0
3.66667
Impossible
Impossible
2.85595

Added by:	Camilo Andrés Varela León
Date:	2007-07-26
Time limit:	3s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Japan Domestic, 2005

SPOJ Problem Set ()

1701. Earth Observation with a Mobile Robot Team

Problem code: EOWAMRT

A new type of mobile robot has been developed for environmental earth observation. It moves around on the ground, acquiring and recording various sorts of observational data using high precision sensors. Robots of this type have short range wireless communication devices and can exchange observational data with ones nearby. They also have large capacity memory units, on which they record data observed by themselves and those received from others.

Figure 1 illustrates the current positions of three robots A, B, and C and the geographic coverage of their wireless devices. Each circle represents the wireless coverage of a robot, with its center representing the position of the robot. In this figure, two robots A and B are in the positions where A can transmit data to B, and vice versa. In contrast, C cannot communicate with A or B, since it is too remote from them. Still, however, once B moves towards C as in Figure 2, B and C can start communicating with each other. In this manner, B can relay observational data from A to C. Figure 3 shows another example, in which data propagate among several robots instantaneously.

Figure 1: The initial configuration of three robots

Figure 2: Mobile relaying

Figure 3: Instantaneous relaying among multiple robots

As you may notice from these examples, if a team of robots move properly, observational data quickly spread over a large number of them. Your mission is to write a program that simulates how information spreads among robots. Suppose that, regardless of data size, the time necessary for communication is negligible.

Input

The input consists of multiple datasets, each in the following format.

N T R
nickname and travel route of the first robot
nickname and travel route of the second robot
...
nickname and travel route of the N-th robot

The first line contains three integers N, T, and R that are the number of robots, the length of the simulation period, and the maximum distance wireless signals can reach, respectively, and satisfy that 1 <= N <= 100, 1 <= T <= 1000, and 1 <= R <= 10.

The nickname and travel route of each robot are given in the following format.

nickname
t0 x0 y0
t1 vx1 vy1
t2 vx2 vy2
...
tk vxk vyk

Nickname is a character string of length between one and eight that only contains lowercase letters. No two robots in a dataset may have the same nickname. Each of the lines following nickname contains three integers, satisfying the following conditions.

0 = t₀ < t₁ < ... < t_k = T
-10 <= vx₁, vy₁, ..., vx_k, vy_k<= 10

A robot moves around on a two dimensional plane. (x₀, y₀) is the location of the robot at time 0. From time t_i-1 to t_i (0 < i <= k), the velocities in the x and y directions are vx_i and vy_i, respectively. Therefore, the travel route of a robot is piecewise linear. Note that it may self-overlap or self-intersect.

You may assume that each dataset satisfies the following conditions.

The distance between any two robots at time 0 is not exactly R.
The x- and y-coordinates of each robot are always between -500 and 500, inclusive.
Once any robot approaches within R + 10^-6. of any other, the distance between them will become smaller than R - 10^-6. while maintaining the velocities.
Once any robot moves away up to R - 10^-6. of any other, the distance between them will become larger than R + 10^-6. while maintaining the velocities.
If any pair of robots mutually enter the wireless area of the opposite ones at time t and any pair, which may share one or two members with the aforementioned pair, mutually leave the wireless area of the opposite ones at time t', the difference between t and t' is no smaller than 10^-6. time unit, that is, |t - t' | >= 10^-6.

A dataset may include two or more robots that share the same location at the same time. However, you should still consider that they can move with the designated velocities.

The end of the input is indicated by a line containing three zeros.

Output

For each dataset in the input, your program should print the nickname of each robot that have got until time T the observational data originally acquired by the first robot at time 0. Each nickname should be written in a separate line in dictionary order without any superfluous characters such as leading or trailing spaces.

Example

Input:
3 5 10
red
0 0 0
5 0 0
green
0 5 5
5 6 1
blue
0 40 5
5 0 0
3 10 5
atom
0 47 32
5 -10 -7
10 1 0
pluto
0 0 0
7 0 0
10 3 3
gesicht
0 25 7
5 -7 -2
10 -1 10
4 100 7
impulse
0 -500 0
100 10 1
freedom
0 -491 0
100 9 2
destiny
0 -472 0
100 7 4
strike
0 -482 0
100 8 3
0 0 0

Output:
blue
green
red
atom
gesicht
pluto
freedom
impulse
strike

Added by:	Camilo Andrés Varela León
Date:	2007-07-26
Time limit:	2s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	Japan Domestic, 2005

SPOJ Problem Set (classical)

1702. Cleaning Robot

Problem code: CLEANRBT

Here, we want to solve path planning for a mobile robot cleaning a rectangular room floor with furniture.

Consider the room floor paved with square tiles whose size fits the cleaning robot (1 × 1). There are 'clean tiles' and 'dirty tiles', and the robot can change a 'dirty tile' to a 'clean tile' by visiting the tile. Also there may be some obstacles (furniture) whose size fits a tile in the room. If there is an obstacle on a tile, the robot cannot visit it. The robot moves to an adjacent tile with one move. The tile onto which the robot moves must be one of four tiles (i.e., east, west, north or south) adjacent to the tile where the robot is present. The robot may visit a tile twice or more.

Your task is to write a program which computes the minimum number of moves for the robot to change all 'dirty tiles' to 'clean tiles', if ever possible.

Input

IThe input consists of multiple maps, each representing the size and arrangement of the room. A map is given in the following format.

w h
c11 c12 c13 ... c1w
c21 c22 c23 ... c2w
...
ch1 ch2 ch3 ... chw

The integers w and h are the lengths of the two sides of the floor of the room in terms of widths of floor tiles. w and h are less than or equal to 20. The character cyx represents what is initially on the tile with coordinates (x, y) as follows.

'.' : a clean tile
'*' : a dirty tile
'x' : a piece of furniture (obstacle)
'o' : the robot (initial position)

In the map the number of 'dirty tiles' does not exceed 10. There is only one 'robot'.

The end of the input is indicated by a line containing two zeros.

Output

For each map, your program should output a line containing the minimum number of moves. If the map includes 'dirty tiles' which the robot cannot reach, your program should output -1.

Example

Input:
7 5
.......
.o...*.
.......
.*...*.
.......
15 13
.......x.......
...o...x....*..
.......x.......
.......x.......
.......x.......
...............
xxxxx.....xxxxx
...............
.......x.......
.......x.......
.......x.......
..*....x....*..
.......x.......
10 10
..........
..o.......
..........
..........
..........
.....xxxxx
.....x....
.....x.*..
.....x....
.....x....
0 0

Output:
8
49
-1

Added by:	Camilo Andrés Varela León
Date:	2007-07-26
Time limit:	5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Japan Domestic, 2005

SPOJ Problem Set (classical)

1703. ACM (ACronymMaker)

Problem code: ACMAKER

The sadists who design problems for ACM programming contests often like to include the abbre- viation “ACM” somewhere in their problem descriptions. Thus, in years past, the World Finals has had problems involving “Apartment Construction Management,” the “Atheneum of Culture and Movies,” the “Association of Cover Manufacturers,” “ACM Airlines,” the “Association for Computa- tional Marinelife,” and even an insect named “Amelia Cheese Mite.” However, the number of word combinations beginning with A, C, and M that make sense is finite and the problem writers are starting to run out of ideas (it’s hard to think of problems about “Antidisestablishmentarianistic Chthonian Metalinguistics”). Fortunately, modern culture allows more flexibility in designing abbreviations — consider, for example:

GDB — Gnu DeBugger
LINUX — either “LINus’s UniX” or “LINUs’s miniX” or “Linux Is Not UniX”
SNOBOL — StriNg Oriented symBOlic Language
SPITBOL — SPeedy ImplemenTation of snoBOL

The rules used in these examples seem to be:

Insignificant words (such as “of”, “a”, “the”, etc.) are ignored.
The letters of the abbreviation must appear, in the correct order, as an ordered sublist of the letters in the significant words of the phrase to be abbreviated.
At least one letter of the abbreviation must come from every significant word (multiple occurrences of a letter are, of course, treated as distinct).

Of course these rules are often broken in real life. For instance, RADAR is an abbreviation for “RAdio Detecting And Ranging”. Under our rules (assuming that “and” is an insignificant word), this would not be a valid abbreviation (however, RADR or RADRAN or DODGING would be valid). You have been asked to take a list of insignificant words and a list of abbreviations and phrases and to determine in how many ways each abbreviation can be formed from the corresponding phrase according to the rules above.

Input

The input file consists of multiple scenarios. Each scenario begins with an integer 100 >= n >= 1 followed by n insignificant words, all in lower case, one per line with no extra white space. (A line containing 0 indicates end of input.) Following this are one or more test cases for this scenario, one per line, followed by a line containing the phrase “LAST CASE”. Each line containing a test case begins with an abbreviation (uppercase letters only) followed by a phrase (lowercase letters and spaces only). The abbreviation has length at least 1 and the phrase contains at least one significant word. No input line (including abbreviation, phrase, and spaces) will contain more than 150 characters. Within these limits, however, abbreviations and phrase words may be any length.

Output

For each test case, output the abbreviation followed by either

is not a valid abbreviation

can be formed in i ways

where i is the number of different ways in which the letters of the abbreviation may be assigned to the letters in the phrase according to the rules above. The value of i will not exceed the range of a 32-bit signed integer.

Example

Input:
2
and
of
ACM academy of computer makers
RADAR radio detection and ranging
LAST CASE
2
a
an
APPLY an apple a day
LAST CASE
0

Output:
ACM can be formed in 2 ways
RADAR is not a valid abbreviation
APPLY can be formed in 1 ways

Added by:	Camilo Andrés Varela León
Date:	2007-07-26
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	East Central North America 2005

SPOJ Problem Set (classical)

1704. Countdown

Problem code: CDOWN

Ann Sister owns a genealogical database service, which maintains family tree history for her clients. When clients login to the system, they are presented with a variety of services: searching, printing, querying, etc. One recent question that came up which the system was not quite prepared for was the following: “Which member of my family had the most grandchildren?” The client who posed this question eventually had to answer it by manually searching the family tree database herself. Ann decided to have software written in case this question (or ones similar to it asking for great-grandchildren, or great-great-grandchildren, etc.) is asked in the future.

Input

Input will consist of multiple test cases. The first line of the input will contain a single integer indicating the number of test cases. Each test case starts with a single line containing two positive integers n and d, where n indicates the number of lines to follow containing information about the family tree, and d indicates the specific question being asked about the tree: if d = 1, then we are interested in persons with the most children (1 generation away); if d = 2, then we are interested in persons with the most grandchildren (2 generations away), and so on. The next n lines are of the form

name m dname₁ dname₂ ... dname_m

where name is one of the family members’ names, m is the number of his/her children, and dname₁ through dname_m are the names of the children. These lines will be given in no particular order. You may assume that all n lines describe one single, connected tree. There will be no more than 1000 people in any one tree, and all names will be at most 10 characters long.

Output

For each test case, output the three names with the largest number of specified descendants in order of number of descendants. If there are ties, output the names within the tie in alphabetical order. Print fewer than three names if there are fewer than three people who match the problem criteria (you should not print anyone’s name who has 0 of the specified descendants), and print more than three if there is a tie near the bottom of the list. Print each name one per line, followed by a single space and then the number of specified descendants. The output for each test case should start with the line

Tree i:

where i is the test case number (starting at 1). Separate the output for each problem with a blank line.

Example

Input:
3
8 2
Barney 2 Fred Ginger
Ingrid 1 Nolan
Cindy 1 Hal
Jeff 2 Oliva Peter
Don 2 Ingrid Jeff
Fred 1 Kathy
Andrea 4 Barney Cindy Don Eloise
Hal 2 Lionel Mary
6 1
Phillip 5 Jim Phil Jane Joe Paul
Jim 1 Jimmy
Phil 1 Philly
Jane 1 Janey
Joe 1 Joey
Paul 1 Pauly
6 2
Phillip 5 Jim Phil Jane Joe Paul
Jim 1 Jimmy
Phil 1 Philly
Jane 1 Janey
Joe 1 Joey
Paul 1 Pauly

Output:
Tree 1:
Andrea 5
Don 3
Cindy 2
Tree 2:
Phillip 5
Jane 1
Jim 1
Joe 1
Paul 1
Phil 1
Tree 3:
Phillip 5

Added by:	Camilo Andrés Varela León
Date:	2007-07-26
Time limit:	3s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	East Central North America 2005

SPOJ Problem Set ()

1705. The Game of Efil

Problem code: GAMEFIL

Almost anyone who has ever taken a class in computer science is familiar with the “Game of Life,” John Conway’s cellular automata with extremely simple rules of birth, survival, and death that can give rise to astonishing complexity.

The game is played on a rectangular field of cells, each of which has eight neighbors (adjacent cells). A cell is either occupied or not. The rules for deriving a generation from the previous one are:

If an occupied cell has 0, 1, 4, 5, 6, 7, or 8 occupied neighbors, the organism dies (0, 1: of loneliness; 4 thru 8: of overcrowding).
If an occupied cell has two or three occupied neighbors, the organism survives to the next gener- ation.
If an unoccupied cell has three occupied neighbors, it becomes occupied (a birth occurs).

One of the major problems researchers have looked at over the years is the existence of so-called “Garden of Eden” configurations in the Game of Life — configurations that could not have arisen as the result of the application of the rules to some previous configuration. We’re going to extend this question, which we’ll call the “Game of Efil”: Given a starting configuration, how many possible parent configurations could it have? To make matters easier, we assume a finite grid in which edge and corner cells “wrap around” (i.e., a toroidal surface). For instance, the 2 by 3 configuration:

subir imagenes

has exactly three possible parent configurations; they are:

subir imagenes

You should note that when counting neighbors of a cell, another cell may be counted as a neighbor more than once, if it touches the given cell on more than one side due to the wrap around. This is the case for the configurations above.

Input

There will be multiple test cases. Each case will start with a line containing a pair of positive integers m and n, indicating the number of rows and columns of the configuration, respectively. The next line will contain a nonnegative integer k indicating the number of “live” cells in the configuration. The following k lines each contain the row and column number of one live cell, where row and column numbering both start at zero. The final test case is followed by a line where m = n = 0 — this line should not be processed. You may assume that the product of m and n is no more than 16.

Output

For each test case you should print one line of output containing the case number and the number of possible ancestors. Imitate the sample output below. Note that if there are 0 ancestors, you should print out

Garden of Eden.

Example

Input:
2 3
2
0 0
0 1
3 3
4
0 0
0 1
0 2
1 1
3 3
5
0 0
1 0
1 2
2 1
2 2
0 0

Output:
Case 1: 3 possible ancestors.
Case 2: 1 possible ancestors.
Case 3: Garden of Eden.

Added by:	Camilo Andrés Varela León
Date:	2007-07-26
Time limit:	60s-65s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	East Central North America 2005

SPOJ Problem Set (classical)

1706. Queens, Knights and Pawns

Problem code: QKP

You all are familiar with the famous 8-queens problem which asks you to place 8 queens on a chess board so no two attack each other. In this problem, you will be given locations of queens and knights and pawns and asked to find how many of the unoccupied squares on the board are not under attack from either a queen or a knight (or both). We’ll call such squares “safe” squares. Here, pawns will only serve as blockers and have no capturing ability. The board below has 6 safe squares. (The shaded squares are safe.)

Recall that a knight moves to any unoccupied square that is on the opposite corner of a 2x3 rectangle from its current position; a queen moves to any square that is visible in any of the eight horizontal, vertical, and diagonal directions from the current position. Note that the movement of a queen can be blocked by another piece, while a knight’s movement can not.

Input

There will be multiple test cases. Each test case will consist of 4 lines. The first line will contain two integers n and m, indicating the dimensions of the board, giving rows and columns, respectively. Neither integer will exceed 1000. The next three lines will each be of the form

k r₁ c₁ r₂ c₂ · · · r_k c_k

indicating the location of the queens, knights and pawns, respectively. The numbering of the rows and columns will start at one. There will be no more than 100 of any one piece. Values of n = m = 0 indicate end of input.

Output

Each test case should generate one line of the form

Board b has s safe squares.

where b is the number of the board (starting at one) and you supply the correct value for s.

Example

4 4
2 1 4 2 4
1 1 2
1 2 3
2 3
1 1 2
1 1 1
0
1000 1000
1 3 3
0
0
0 0

Output:
Board 1 has 6 safe squares.
Board 2 has 0 safe squares.
Board 3 has 996998 safe squares.

Added by:	Camilo Andrés Varela León
Date:	2007-07-26
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	East Central North America 2005

SPOJ Problem Set (classical)

1707. Reliable Nets

Problem code: RELINETS

You’re in charge of designing a campus network between buildings and are very worried about its reliability and its cost. So, you’ve decided to build some redundancy into your network while keeping it as inexpensive as possible. Specifically, you want to build the cheapest network so that if any one line is broken, all buildings can still communicate. We’ll call this a minimal reliable net.

Input

There will be multiple test cases for this problem. Each test case will start with a pair of integers n (<=15) and m (<= 20) on a line indicating the number of buildings (numbered 1 through n) and the number of potential inter-building connections, respectively. (Values of n = m = 0 indicate the end of the problem.) The following m lines are of the form b₁ b₂ c (all positive integers) indicating that it costs c to connect building b₁ and b₂. All connections are bidirectional.

Output

For each test case you should print one line giving the cost of a minimal reliable net. If there is a minimal reliable net, the output line should be of the form:

The minimal cost for test case p is c.

where p is the number of the test case (starting at 1) and c is the cost. If there is no reliable net possible, output a line of the form:

There is no reliable net possible for test case p.

Example

Input:
4 5
1 2 1
1 3 2
2 4 2
3 4 1
2 3 1
2 1
1 2 5
0 0

Output:
The minimal cost for test case 1 is 6.
There is no reliable net possible for test case 2.

Added by:	Camilo Andrés Varela León
Date:	2007-07-26
Time limit:	3s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	East Central North America 2005

SPOJ Problem Set (classical)

1708. Square Count

Problem code: SQCOUNT

Little Bobby Roberts, age 8, has been dragged to yet another museum by his parents. While they while away the hours studying Etruscan pottery and Warhol soup cans, Bobby must depend on himself for entertainment. Having a mathematical bent, he recently started counting all the square tiles on the floors of the museum. He soon realized that the tiles could be grouped into larger squares that needed to be added to the count. The problem became a bit more complicated when he started counting squares contained in multiple rooms, since some squares overlapped both rooms. For example, the two rooms shown below contain a total of 86 squares: 45 1 × 1 squares, 28 2 × 2 squares and 13 3 × 3 squares. (Note the opening between the two rooms is only 3 squares wide.)

While this helped kill several days’ worth of museum visits, it soon became rather tedious, so Bobby is now looking for a program to automate the counting process for him.

Input

Input will consist of multiple test cases. The first line of each case will be a positive integer n <= 1000 which will indicate the number of rooms in the museum. After this will be n lines, each containing a description of one room. Each room will be rectangular in shape and will be described by a line of the form

x₁ y₁ x₂ y₂

where (x₁, y₁) and (x₂, y₂) are opposing corner coordinates (integers) of the room. No two rooms will overlap, though they may share a side. If the shared side is of length m > 2, then a door of length m−2 exists between the two rooms, centered along the shared length. No square of any size will overlap more than two rooms. All x and y values will be <= 1, 000, 000. An input line of n = 0 terminates input and should not be processed.

Output

For each test case, output the total number of squares on a single line in the format shown below. All answers will fit within a 32-bit integer and cases are enumerated starting at 1.

Example

Input:
2
0 0 9 3
10 6 4 3
3
11 20 15 24
11 17 15 20
15 16 20 24
0

Output:
Case 1: 86
Case 2: 152

Added by:	Camilo Andrés Varela León
Date:	2007-07-26
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	East Central North America 2005

SPOJ Problem Set (classical)

1709. Swamp Things

Problem code: SWTHIN

Hugh F. Oh, in his never-ending quest to prove the existence of extraterrestrials, has gotten hold of a number of nighttime photographs taken by a research group that is examining glowing swamp gas. Hugh wants to see if any of the photos show, not swamp gas, but Little Grey Men in glowing suits. The photographs consist of bright dots appearing against a black background. Unfortunately, at the time the photos were taken, trains were travelling through the area (there is a train trestle over the swamp), and occasional lights from the train windows also appear in the photographs. Hugh, being a fastidious researcher, wants to eliminate these spots from the images. He can’t tell from the photos exactly where the tracks are, or from what direction the photos were taken, but he knows that the tracks in that area are perfectly straight, so he’s decided on the following approach: he will find the line with the maximum number of spots lying on it and, if there are four or more spots on the line, he will eliminate those points from his calculations, assuming that those are windows on the train. If two or more lines have the maximum number of points, Hugh will just randomly select one such set and delete it from the photo (he’s not all that fastidious – after all, he believes in Little Grey Men). If there are fewer than four points lying along a common line, Hugh will assume that there is no train in the photograph and won’t delete any points. Please write a program for him to process a set of photographs.

Input

There will be a series of test cases. Each test case is one photograph described by a line containing a positive integer n (<= 1000) the number of distinct spots in the photograph, followed by n lines containing the integer coordinates of the spots, one (x, y) pair per line. All coordinates are between 0 and 10000. The last photo description is followed by a line containing a zero, marking the end of the input. This line should not be processed.

Output

For each test case, output the photo number followed by the number of points eliminated from the photograph. Imitate the sample output below.

Example

Input:
6
0 1
0 2
1 2
2 2
4 5
5 6
4
3 5
4 4
6 5
7 4
0

Output:
Photo 1: 4 points eliminated
Photo 2: 0 points eliminated

Added by:	Camilo Andrés Varela León
Date:	2007-07-26
Time limit:	25s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	East Central North America 2005

SPOJ Problem Set (classical)

1710. Two Ends

Problem code: TWENDS

In the two-player game “Two Ends”, an even number of cards is laid out in a row. On each card, face up, is written a positive integer. Players take turns removing a card from either end of the row and placing the card in their pile. The player whose cards add up to the highest number wins the game. Now one strategy is to simply pick the card at the end that is the largest — we’ll call this the greedy strategy. However, this is not always optimal, as the following example shows: (The first player would win if she would first pick the 3 instead of the 4.)

3 2 10 4

You are to determine exactly how bad the greedy strategy is for different games when the second player uses it but the first player is free to use any strategy she wishes.

Input

There will be multiple test cases. Each test case will be contained on one line. Each line will start with an even integer n followed by n positive integers. A value of n = 0 indicates end of input. You may assume that n is no more than 1000. Furthermore, you may assume that the sum of the numbers in the list does not exceed 1,000,000.

Output

For each test case you should print one line of output of the form:

In game m, the greedy strategy might lose by as many as p points.

where m is the number of the game (starting at game 1) and p is the maximum possible difference between the first player’s score and second player’s score when the second player uses the greedy strategy. When employing the greedy strategy, always take the larger end. If there is a tie, remove the left end.

Example

Input:
4 3 2 10 4
8 1 2 3 4 5 6 7 8
8 2 2 1 5 3 8 7 3
0

Output:
In game 1, the greedy strategy might lose by as many as 7 points.
In game 2, the greedy strategy might lose by as many as 4 points.
In game 3, the greedy strategy might lose by as many as 5 points.

Added by:	Camilo Andrés Varela León
Date:	2007-07-26
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	East Central North America 2005

SPOJ Problem Set (classical)

1712. Permalex

Problem code: PRMLX

Given a string of characters, we can permute the individual characters to make new strings. If we can impose an ordering on the characters (say alphabetic sequence), then the strings themselves can be ordered and any given permutation can be given a unique number designating its position in that ordering. For example the string `acab' gives rise to the following 12 distinct permutations:

aabc	1	acab	5	bcaa	9
aacb	2	acba	6	caab	10
abac	3	baac	7	caba	11
abca	4	baca	8	cbaa	12

Thus the string `acab' can be characterised in this sequence as 5.

Write a program that will read in a string and determine its position in the ordered sequence of permutations of its constituent characters. Note that numbers of permutations can get very large; however we guarantee that no string will be given whose position is more than 2^31 = 2.147.483.647

Input and Output

Input will consist of a series of lines, each line containing one string. Each string will consist of up to 30 lower case letters, not necessarily distinct. Test cases a separated by empty lines. The file will be terminated by a line consisting of a single #.

Output will consist of a series of lines, one for each line of the input. Each line will consist of the position of the string in its sequence, right justified in a field of width 10.

Sample Input

bacaa
abc
cba

bacaa
abc
cba
#

Sample Output

Added by:	Andrés Leonardo Rojas Duarte
Date:	2007-07-27
Time limit:	5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	ACM ICPC 1992 Northwestern European Regionals

SPOJ Problem Set (classical)

1713. Funny scales

Problem code: SCALE

Kinh_Can has a set of precious weights P₁, P₂, ..., P_N in which the mass of the i^th weight is P_i = 3^i-1, and a balance with 2 scales. On a nice day, Kinh_Can decided to show off his set of precious weights to his friends, and said that he can put them in equilibrium with any weight as long as its mass is not more than the mass of the sum of his weights. At first, his friends didn't believe, but after many trials they realized that Kinh_Can was right. In addition, while putting a thing whose mass is X on a scale, Kinh_Can could put right away the weights added on the 2 scales to keep their blance without any trial. With a random weight X (X is a natural number, X ≠ 0). Your task is to put weights on scales in order to keep the 2 scales' balance like Kinh_Can. The first scale initially weights X, and the second one weights 0.

Input

Input has exactly one line consisting 2 numbers, the first is N and the second is X.

Output

If there is no solution, you should write -1
If there is at least one solution for the problem, you should write exactly 2 lines:
- The first line contains some numbers descripting the indices of the weights in the first disc
- The second line contains some numbers description the indices of the weights in the second disc
- Note: One of 2 lines can be blank

Constraints

1 ≤ N ≤ 20
1 ≤ X ≤ 2000000000

Example

Input 1:
10 2

Output 1:
1
2

Input 2:
10 5

Output 2:
1 2
3

Added by:	Unknown
Date:	2007-07-29
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Classical

SPOJ Problem Set (classical)

1715. Another Necklace Problem

Problem code: NCKLCE

T Corporation is a company which produces colorful necklaces. The necklaces designed by them are unique and fashionable, and because of the price, they are popular with the youth. Now, T Corporation intends to design a self-help Producing System.

This system includes hardware and software. The software is interactive and controls the hardware. Now the hardware has been completed, but the software is to develop. The workers find you, who is taking NOI. Could you please write a software system to simulate?

A necklace includes N beads. The color of each bead is one of 1..c. The necklace is fixed in a plain. One position of the plain is marked as Position 1, and the other positions are marked as 2..n in clockwise.
Your system should supply the orders as follow:

+------------+-------------------------------+--------------------------------------------------+
|Order       |Parameters restrictions        |Content                                           |
+------------+-------------------------------+--------------------------------------------------+
|R  k        |0 < k < N                      |It means Rotate K. Rotate the necklace by k       |
|            |                               |positions in clockwise. i.e. The bead in former 1 |
|            |                               |position will be transfer to position k+1, the    |
|            |                               |bead in former 2 position will be transfer to     |
|            |                               |position k+2, and so on.                          |
+------------+-------------------------------+--------------------------------------------------+
|F           |                               |It means Flip. Flip the plain by the given axis.  |
|            |                               |The bead in position 1 doesn't move.The bead in   |
|            |                               |position 2 will swap with the bead in position    |
|            |                               |N,the bead in position 3 will swap with the bead  |
|            |                               |in position n-1, and so on.                       |
+------------+-------------------------------+--------------------------------------------------+
|S i j       |1 <= i,j <= n                  |Swap the bead in position i and j.                |
+------------+-------------------------------+--------------------------------------------------+
|P i j x     |1 <= i,j <= n , x<= c          |It means Paint. Paint color x from position i to  |
|            |                               |position j in clockwise.                          |
+------------+-------------------------------+--------------------------------------------------+
|C           |                               |It means Count. Ask how many parts are there in   |
|            |                               |the necklace. We define some consecutive beads    |
|            |                               |in same color as a "part". Pay attention that C is|
|            |                               |different from CS 1,n.                            |
+------------+-------------------------------+--------------------------------------------------+
|CS i j      |1 <= i,j <= n                  |It means CountSegment i,j. Ask how many parts are |
|            |                               |there from position i to position j in clockwise, |
|            |                               |i and j included.                                 |
+------------+-------------------------------+--------------------------------------------------+

Input

The first line in input includes two integers N,C, representing the beads in the necklace and the number of colors. The second line contains N integers x1,x2...xn, representing the colors of beads from position 1 to position n,1<=xi<=c. The third line includes a integer q, as the number of orders. There is an order in the next q lines, as mentioned above.

For 60% test cases, n <= 1000, Q <= 1000;
For 100% test cases, n <= 500000, Q <= 500000.

Output

For every order starts with C and CS, print a integer as the answer.

Example

Input:
5 3
1 2 3 2 1
4
C
R 2
P 5 5 2
CS 4 1

Output:
4
1

Test data is unofficial. If you have any questions, please contact me.

Added by:	Bin Jin
Date:	2007-08-03
Time limit:	0.100s-5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C++ 4.0.0-8
Resource:	Chinese National Olympiad in Informatics 2007,Day 2

SPOJ Problem Set (classical)

1716. Can you answer these queries III

Problem code: GSS3

You are given a sequence A of N (N <= 50000) integers between -10000 and 10000. On this sequence you have to apply M (M <= 50000) operations:
modify the i-th element in the sequence or for given x y print max{Ai + Ai+1 + .. + Aj | x<=i<=j<=y }.

Input

The first line of input contains an integer N. The following line contains N integers, representing the sequence A1..AN.
The third line contains an integer M. The next M lines contain the operations in following form:
0 x y: modify Ax into y (|y|<=10000).
1 x y: print max{Ai + Ai+1 + .. + Aj | x<=i<=j<=y }.

Output

For each query, print an integer as the problem required.

Example

Input:
4
1 2 3 4
4
1 1 3
0 3 -3
1 2 4
1 3 3

Output:
6
4
-3

Added by:	Bin Jin
Date:	2007-08-03
Time limit:	2s
Source limit:	5000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C++ 4.0.0-8
Resource:	own problem

SPOJ Problem Set (classical)

1722. Life, the Universe, and Everything II

Problem code: RP

This problem tests your mathematic knowledge and your programming ability very much. Your task is to calculate the number of different Minimum Spanning Trees (MSTs) of a special undirected unweighted graph. The graph has n nodes numbered from 1 to n, and there is an edge between node i (1<=i<=n) and node j (1<=j<=n) if and only if 0<|i-j|<=k.

Input

Multiple test cases, the number of them(<=8) is given in the very first line.

Each test case contains one line with two space-separated numbers k(1<=k<=5) and n(1<=n<=10¹⁵).

Output

For each test case you should output one line, the number of different MSTs of the corresponding graph modulo 65521.

Example

Input:
1
3 5

Output:
75

Added by:	[Trichromatic] XilinX
Date:	2007-08-04
Time limit:	1s-4s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2007,Day 2; Translated by Blue Mary

SPOJ Problem Set (classical)

1723. Bee Maja

Problem code: BMJ

Documento sin título

Maja is a bee. She lives in a bee hive with thousands of other bees. This bee hive consists of many hexagonal honey combs where the honey is stored in.
But bee Maja has a problem. Willi told her where she can meet him, but because Willi is a male drone and Maja is a female worker they have different coordinate systems.

Maja's Coordinate System

Willi's Coordinate System

Maja who often flies directly to a special honey comb has laid an advanced two dimensional grid over the whole hive.

Maja

Willi who is more lazy and often walks around just numbered the cells clockwise starting from 1 in the middle of the hive.

Willi

Help Maja to convert Willi's system to hers. Write a program which for a given honey comb number gives the coordinates in Maja's system.

Input

The input contains one or more integers which represent Willi's numbers. Each number stands on its own in a separate line, directly followed by a newline. The honey comb numbers are all less than 100 000.

Output

You should output the corresponding Maja coordinates to Willi's numbers, each coordinate pair on a separate line.

Sample Input

1
2
3
4
5

Sample Output

0 0
0 1
-1 1
-1 0
0 -1

Added by:	Andrés Leonardo Rojas Duarte
Date:	2007-08-04
Time limit:	20s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Ulm Local 1999

SPOJ Problem Set (classical)

1724. Counting Triangles

Problem code: TRICOUNT

We define the LEVEL of a triangle as in the following illustrative image:

Task: Your task is very easy. All you have to do is to count all triangles in the biggest one (Level N).

Input

The first line of the input contains an integer T (T ≤ 10000) - the number of test cases and T lines follow. Each line contains an integer N (1 ≤ N ≤ 10⁶) which is the level of the triangle in that test case.

Output

For each test case, you should write a seperate line: the number of triangles in the biggest one (Level N). (All answers will fit within the range of a 64-bit integer)

Example

Input:
3
1
2
3

Output:
1
5
13

Added by:	Unknown
Date:	2007-08-05
Time limit:	1s
Source limit:	500B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Trần Huy Hưng

SPOJ Problem Set (classical)

1725. The Importance

Problem code: IMPORT1

Given an undirected weighted graph {V,E}. Your task to calculate the importance of each node.

The importance of a node v (I(v)) can be defined as follow:

C_s,t is the number of different shortest paths from s to t, C_s,t(v) is the number of different shortest paths from s to t through v.

Input

Multiple test cases, the number of them is given in the very first line.

For each test case:

The first line contains two space-separated integers n(n<=100) and m(m<=4500), the number of nodes in the graph and the number of edges in the graph. The nodes are numbered from 1 to n. m lines follow, each contains 3 integers a, b, c, 1<=a, b<=n, 1<=c<=1000, a!=b, which denotes that there is an undirected edge between node a and node b weighted c. You may assume that there is at most one edge between any pair of nodes, and the number of shortest paths between any pair of nodes is at least 1 and at most 10¹⁰.

Output

For each test case:

Your Output should contains n lines, each contains one single real number, with 3 decimal places after radix point. The number in the ith line denotes the importance of the ith node.

Example

Input:
1
4 4
1 2 1
2 3 1
3 4 1
4 1 1

Output:
1.000
1.000
1.000
1.000

Added by:	[Trichromatic] XilinX
Date:	2007-08-05
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2007,Day 1; Translated by Blue Mary

SPOJ Problem Set (classical)

1726. Exchange

Problem code: EXCHANGE

There are 3 kinds of money in a planet far away from the earth: Mone, Luck, and Rpin. There's a money exchange company in this planet. You must go to this company if you want to do some money exchange, and, more autocratically, this company regulate the exchange rate of each pair of these 3 kinds of money.

The money exchange will be done in the following two ways:

(A)

You give the company a real number x in the range (0,100], the company will exchange x% of your Mone and x% of your Luck to equal Rpin according to the exchange rate of that day.

(B)

You give the company a real number x, the company will exchange your x Rpin to some Mone and Luck, whose value is equal to x Rpin according to the exchange rate of that day, and, the value of Mone is Rate times of the value of Luck.

You can do many exchange operations in the same day.

Now, as the excellant spy in this planet, you know the exchange rate between Mone and Rpin of each of the next n days(a_i Mone per Rpin), and the exchange rate between Luck and Rpin of each of the next n days(b_i Luck per Rpin), and, each Rate of the next n days( Rate_i). you have S Rpin in the start, and you want to get most Rpin in the nth day later.

Input

Multiple test cases, the number of them( <=5 ) is given in the very first line.

For each test case:

The first line contains a integer number n(1<=n<=100000) and a real number S.n lines follow, each contains 3 real numbers: a_i(between 0 and 10), b_i(between 0 and 10), Rate_i(between 0 and 100).

Output

For each test case, output one line contains a real number with 3 digits after decimal point, which denotes to the answer. You can assume it is less than 1000000000.

Example

Input:
1
3 100
1 1 1
1 2 2
2 2 3

Output:
225.000

Warning: large input/output data, be careful with certain languages; the time limit is somewhat strict for this problem

Added by:	[Trichromatic] XilinX
Date:	2007-08-05
Time limit:	2s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Chinese National Olympiad in Informatics 2007,Day 1; Translated by Blue Mary

SPOJ Problem Set (classical)

1728. Common Permutation

Problem code: CPRMT

Given two strings of lowercase letters, a and b, print the longest string x of lowercase letters such that there is a permutation of x that is a subsequence of a and there is a permutation of x that is a subsequence of b.

Input

Input file contains several lines of input. Consecutive two lines make a set of input. That means in the input file line 1 and 2 is a set of input, line 3 and 4 is a set of input and so on. The first line of a pair contains a and the second contains b. Each string is on a separate line and consists of at most 1000 lowercase letters.

Output

For each set of input, output a line containing x. If several x satisfy the criteria above, choose the first one in alphabetical order.

Example

Sample input:
pretty
women
walking
down
the
street
 
Sample output:
e
nw
et

Added by:	Andrés Leonardo Rojas Duarte
Date:	2007-08-05
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	University of Alberta Local Contest 1999

SPOJ Problem Set ()

1730. Counting Triangles II

Problem code: TCOUNT2

We define the LEVEL of a triangle as in the following illustrative image:

And we continue defining the LEVEL of a hexagon. It's called level N hexagon if it’s joined by 6 triangles, each one is a level N triangle.

Task: All you have to do is to count all triangles in the “level N” hexagon.

Input

The first line of the input contains an integer T - the number of test cases and T lines follow. Each line contains an integer N which is the level of the hexagon in that test case.

Output

For each test case, you should write a seperate line: the number of triangles in the “level N” hexagon. (All answers will fit within the range of a 64-bit positive integer)

Example

Input:
1
1

Output:
6

Be careful with certain languages

Added by:	Unknown
Date:	2007-08-06
Time limit:	1s
Source limit:	300B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	ASM C C++ 4.0.0-8 C99 strict D PAS fpc PAS gpc
Resource:	Trần Huy Hưng

SPOJ Problem Set (classical)

1731. Counting Triangles III

Problem code: TCOUNT3

Have you felt bored when counting triangles?

Like TRICOUNT and TCOUNT2, we define the LEVEL of a triangle as in the following illustrative image:

And now we will continue defining the LEVEL of a hexagram. It's called level N hexagram if it’s joined by 12 triangles, each one is a level N triangle.

Task: All you have to do is to count all triangles in the level N hexagram.

Input

The first line of the input contains an integer T - the number of test cases and T lines follow. Each line contains an integer N which is the level of the hexagram in that test case.

Output

For each test case, you should write a seperate line: the number of triangles in the level N hexagram. (All answers will fit within the range of a 64-bit positive integer)

Example

Input:
1
1

Output:
20

The author allows only few languages

Added by:	Unknown
Date:	2007-08-07
Time limit:	1s
Source limit:	128B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	ASM C C++ 4.0.0-8 C99 strict D PAS fpc PAS gpc PERL PYTH 2.7 RUBY
Resource:	Trần Huy Hưng

SPOJ Problem Set (classical)

1739. Yet Another Equation

Problem code: EQU2

Consider the equation

x² - ny² = 1

where n is some integer.

Find the smallest strictly positive integer solutions (x, y) for a given n.

Input

The number of test cases t (around 30), followed by a list of t values of n (2 ≤ n ≤ 1000). You can assume that the equation can be solved for all values of n in the input set.

Output

For every test case, the values of x and y separated by a space character, on separate lines.

Example

Input:
3
2
6
61

Output:
3 2
5 2
1766319049 226153980

Added by:	Mauro Persano
Date:	2007-08-18
Time limit:	5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Brahmagupta, circa 628 AD

SPOJ Problem Set (classical)

1741. Tetris 3D

Problem code: TETRIS3D

The authors of the game "Tetris" have decided to make a new, three-dimensional version, in which cuboids would fall down on a rectangular platform. The blocks fall down separately in a certain order, just like in the two-dimensional game. A block falls down until it reaches an obstacle: the platform or another block, that has already stopped - then it stops and remains in this exact position till the game is over.
However, the authors wanted to change the spirit of the game, turning it from a simple arcade-game into a play far more puzzling. Knowing the order of the falling blocks and their flight path the player's task is to tell the height of the highest point of the arrangement after all blocks have fallen down (and stopped). All the blocks are falling down vertically and do not rotate while falling. For convenience we'll introduce a cartesian coordinate system on the platform, with the center in one of the platform's corners and the axes parallel to the platform's edges.
Write a program that:
• reads the descriptions of subsequent falling blocks from the standard input,
• determines the height of the highest point of the arrangement of blocks after all have fallen down and stopped,
• writes the result to the standard output.

Input

In the first line of the input there are three integers D, S and N ( 1<=N<=20 000, 1<=D, S<=1 000), separated by single spaces and denoting respectively: the length and the depth of the platform and the number of blocks that are going to fall down on it. In the following N lines the descriptions of subsequent blocks are given, one in each line.
Each description of a block consists of five integers: d, s, w, x and y (1<=d, 0<=x,d+x<=D, 1<=s,0<=y,s+y<=S, 1<=w<=100 000), representing a block of length d depth s and height w This very block will be falling down on the platform with its d×s face as the bottom, where the length and depth of the block are parallel to those of the platform. The coordinates of the vertices of the projection of the block on the platform are: (x, y), (x + d, y), (x, y + s) and (x + d, y + s).

Output

The first and only line of the standard output should contain exactly one integer, the height of the highest point of the arrangement of blocks after all have fallen down ad stopped.

Example

Input:
7 5 4
4 3 2 0 0
3 3 1 3 0
7 1 2 0 3
2 3 3 2 2

Output:
6

Added by:	Bin Jin
Date:	2007-08-19
Time limit:	2s-4s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C++ 4.0.0-8
Resource:	POI XIII - Stage I

SPOJ Problem Set (classical)

1744. Evaluate the polynomial

Problem code: POLEVAL

Your task consists of evaluate a polynomial of degree n (0 <= n <= 999) represented by its n+1 coefficients of the form:

p_n(x) = c_nxⁿ + c_n-1x^n-1 + … + c₂x² + c₁x + c₀

in each one of the k (1 <= k <= 100) points x₁, x₂, …, x_k. The coefficients of the polynomial and the values where they will be evaluated are integers in the interval [-100, 100] that guarantees that the polynomial's evaluation is at the most 2⁶³ – 1.

Input

There will be multiple test cases, each one with 4 lines that are described below
n: degree of polynomial.
c_n c_n-1… c₂ c₁ c₀: coefficients of the polynomial separated by a single space.
k: number of points to evaluate the polynomial.
x₁ x₂… x_k-1 x_k: points to evaluate the polynomial separated by a single space.

The final test case is a single line where n = -1 and this case should not be processed.

Output

For each test case you should print k + 1 lines of output, the very first line containing the case number and the following k lines with the result of the polynomial's evaluation in each one of the k given points. See the sample.

Example

Input:
2
1 -2 -1
5
0 1 -1 2 -2
3
2 1 -2 -1
4
0 -1 2 -2
-1

Output:
Case 1:
-1
-2
2
-1
7
Case 2:
-1
0
15
-9

Added by:	Ivan Alfonso Olamendy
Date:	2007-08-25
Time limit:	2.5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS NODEJS PERL 6
Resource:	My own resource

SPOJ Problem Set (classical)

1748. Sequence Partitioning II

Problem code: SEQPAR2

Given a sequence of N ordered pairs of positive integers (A_i, B_i), you have to partition it into several contiguous parts. Let p be the number of these parts, whose boundaries are (l₁, r₁), (l₂, r₂), ... ,(l_p, r_p), which satisfy l_i= r_i-₁+ 1, l_i<= r_i, l₁= 1, r_p= n. The parts themselves also satisfy the following restrictions:

For any two pairs (A_p, B_p), (A_q, B_q), where (A_p, B_p) is belongs to the T_pth part and (A_q, B_q) the T_qth part. If T_p < T_q, then B_p> A_q.
Let M_i be the maximum A-component of elements in the ith part, say
M_i = max {A_{l_i}, A_{l_i+}_₁, ..., A_{r_i}}, 1 <= i <= p
it is provided that

where Limit is a given integer.

Let S_i be the sum of B-components of elements in the ith part.

Now I want to minimize the value

max{S_i:1 <= i <= p}

Could you tell me the minimum?

Input

The input contains exactly one test case. The first line of input contains two positive integers N (N <= 50000), Limit (Limit <= 2³¹-1). Then follow N lines each contains a positive integers pair (A, B). It's always guaranteed that

max{A₁, A₂, ..., A_n} <= Limit

Output

Output the minimum target value.

Example

Input:
4 6
4 3
3 5
2 5
2 4

Output:
9

Explanation

An available assignment is the first two pairs are assigned into the first part and the last two pairs are assigned into the second part. Then B₁ > A₃, B₁ > A₄, B₂ > A₃, B₂ > A₄, max{A₁, A₂}+max{A₃, A₄} <= 6, and minimum max {B₁+B₂, B₃+B₄}=9.

Added by:	Bin Jin
Date:	2007-08-28
Time limit:	1s-15s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C++ 4.0.0-8
Resource:	POJ Monthly--2007.07.08

SPOJ Problem Set (classical)

1754. Divisor Summation (Hard)

Problem code: DIVSUM2

Given a natural number n (1 <= n <= 1e16), please output the summation of all its proper divisors.

Definition: A proper divisor of a natural number is the divisor that is strictly less than the number.

e.g. number 20 has 5 proper divisors: 1, 2, 4, 5, 10, and the divisor summation is: 1 + 2 + 4 + 5 + 10 = 22.

Input

An integer stating the number of test cases (equal to 500), and that many lines follow, each containing one integer between 1 and 1e16 inclusive.

Output

One integer each line: the divisor summation of the integer given respectively.

Example

Input:
3
2
10
20

Output:
1
8
22

warning: a naive algorithm may not run in time.

Added by:	Bin Jin
Date:	2007-08-29
Time limit:	60s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C++ 4.0.0-8
Resource:	own problem

SPOJ Problem Set (classical)

1771. Yet Another N-Queen Problem

Problem code: NQUEEN

After solving Solution to the n Queens Puzzle by constructing, LoadingTime wants to solve a harder version of the N-Queen Problem. Some queens have been set on particular locations on the board in this problem. Can you help him??

Input

The input contains multiple test cases. Every line begins with an integer N (N<=50), then N integers followed, representing the column number of the queen in each rows. If the number is 0, it means no queen has been set on this row. You can assume there is at least one solution.

Output

For each test case, print a line consists of N numbers separated by spaces, representing the column number of the queen in each row. If there are more than one answer, print any one of them.

Example

Input:
4 0 0 0 0
8 2 0 0 0 4 0 0 0

Output:
2 4 1 3
2 6 1 7 4 8 3 5

Added by:	Bin Jin
Date:	2007-09-06
Time limit:	5s
Source limit:	10000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C++ 4.0.0-8
Resource:	own problem

SPOJ Problem Set ()

1772. Find The Determinant II

Problem code: DETER2

In this problem you have to calculate the determinant of an N x N matrix whose entries are given by m[i][j] = gcd(i,j)^k, 1 ≤ i,j ≤ N.

Here gcd(i,j) denotes the greatest common divisor of i and j.

As the determinant D can grow very large, you have to print D%1000003.

Input

First line of input consists of a single integer containing the number of test cases T ( equal to around 20), each of the following T lines contain two integers N and k where N is the size of the matrix and k is the exponent.
1 ≤ N ≤ 1000000
1 ≤ k ≤ 10⁹

Output

One line corresponding to each test case containing the determinant modulo 1000003 for the corresponding test case.

Example

Input:
3
4 2
2 4
4 3


Output:
288
15
10192

Note: You may want to solve DETER first, in case you havent already solved it.

Added by:	Ajay Somani
Date:	2007-09-07
Time limit:	1s
Source limit:	2048B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	"The Art of Computer Programming"

SPOJ Problem Set (classical)

1774. All Discs Considered

Problem code: ALL

Operating systems are large software artefacts composed of many packages, usually distributed on several media, e.g., discs. You probably remember the time when your favourite operating system was delivered on 21 floppy discs, or, a few years later, on 6 CDs. Nowadays, it will be shipped on several DVDs, each containing tens of thousands of packages.

The installation of certain packages may require that other packages have been installed previously. Therefore, if the packages are distributed on the media in an unsuitable way, the installation of the complete system requires you to perform many media changes, provided that there is only one reading device available, e.g., one DVD-ROM drive. Since you have to start the installation somehow, there will of course be one or more packages that can be installed independently of all other packages.

Given a distribution of packages on media and a list of dependences between packages, you have to calculate the minimal number of media changes required to install all packages. For your convenience, you may assume that the operating system comes on exactly 2 DVDs.

Input

The input contains several test cases. Every test case starts with three integers N₁, N₂, D. You may assume that 1<=N₁,N₂<=50000 and 0<=D<=100000. The first DVD contains N₁ packages, identified by the numbers 1, 2, ..., N₁. The second DVD contains N₂ packages, identified by the numbers N₁+1, N₁+2, ..., N₁+N₂. Then follow D dependence specifications, each consisting of two integers x_i, y_i. You may assume that 1<=x_i,y_i<=N₁+N₂ for 1<=i<=D. The dependence specification means that the installation of package x_i requires the previous installation of package y_i. You may assume that there are no circular dependences. The last test case is followed by three zeros.

Output

For each test case output on a line the minimal number of DVD changes required to install all packages. By convention, the DVD drive is empty before the installation and the initial insertion of a disc counts as one change. Likewise, the final removal of a disc counts as one change, leaving the DVD drive empty after the installation.

Example

Input:
3 2 1
1 2
2 2 2
1 3
4 2
2 1 1
1 3
0 0 0

Output:
3
4
3

Added by:	Wanderley Guimarăes
Date:	2007-09-14
Time limit:	5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS
Resource:	University of Ulm Local Contest 2004

SPOJ Problem Set (classical)

1775. Boolean Logic

Problem code: BOOLE

Propositions are logical formulas consisting of proposition symbols and connecting operators. They are recursively defined by the following rules:

All proposition symbols (in this problem, lower-case alphabetic characters, e.g., a and z) are propositions.
If P is a proposition, (!P) is a proposition, and P is a direct subformula of it.
If P and Q are propositions, (P&Q), (P|Q), (P-->Q), and (P<->Q) are propositions, and P and Q are direct subformulas of them.
Nothing else is a proposition.

The operations !, &, |, -->, and <-> denote logical negation, conjunction, disjunction, implication, and equivalence, respectively. A proposition P is a subformula of a proposition R if P=R or P is a direct subformula of a proposition Q and Q is a subformula of R.

Let P be a proposition and assign boolean values (i.e., 0 or 1) to all proposition symbols that occur in P. This induces a boolean value to all subformulas of P according to the standard semantics of the logical operators:

negation	conjunction	disjunction	implication	equivalence
`!0`=`1`	`0&0`=`0`	`0\|0`=`0`	`0-->0`=`1`	`0<->0`=`1`
`!1`=`0`	`0&1`=`0`	`0\|1`=`1`	`0-->1`=`1`	`0<->1`=`0`
	`1&0`=`0`	`1\|0`=`1`	`1-->0`=`0`	`1<->0`=`0`
	`1&1`=`1`	`1\|1`=`1`	`1-->1`=`1`	`1<->1`=`1`

This way, a value for P can be calculated. This value depends on the choice of the assignment of boolean values to the proposition symbols. If P contains n different proposition symbols, there are 2ⁿ different assignments. To evaluate all possible assignments we may use truth tables.

A truth table contains one line per assignment (i.e., 2ⁿ lines in total). Every line contains the values of all subformulas under the chosen assignment. The value of a subformula is aligned with the proposition symbol, if the subformula is a proposition symbol, and with the center of the operator otherwise.

Input Specification

The input contains several test cases, each on a separate line. Every test case denotes a proposition and may contain arbitrary amounts of spaces in between. The input file terminates immediately after the newline symbol following the last test case.

Output Specification

For each test case generate a truth table for the denoted proposition. Start the truth table by repeating the input line. Evaluate the proposition (and its subformulas) for all assignments to its variables, and output one line for each assignment. The line must have the same length as the corresponding input line and must consist only of spaces and the characters 0 and 1. Output an empty line after each test case.

Let s₁,...,s_n be the proposition symbols in the denoted proposition sorted in alphabetic order. Then, all assignments of 0 to s₁ must precede the assignments of 1 to s₁. Within each of these blocks of assignments, all assignments of 0 to s₂ must precede the assignments of 1 to s₂, and so on.

Sample Input

((b --> a) <-> ((! a) --> (! b)))
  ((y &  a)   -  ->(c |c))

Sample Output

((b --> a) <-> ((! a) --> (! b)))
  0  1  0   1    1 0   1   1 0   
  1  0  0   1    1 0   0   0 1   
  0  1  1   1    0 1   1   1 0   
  1  1  1   1    0 1   1   0 1   

  ((y &  a)   -  ->(c |c))
    0 0  0       1  0 00  
    1 0  0       1  0 00  
    0 0  0       1  1 11  
    1 0  0       1  1 11  
    0 0  1       1  0 00  
    1 1  1       0  0 00  
    0 0  1       1  1 11  
    1 1  1       1  1 11

Added by:	Wanderley Guimarăes
Date:	2007-09-14
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS
Resource:	University of Ulm Local Contest 2004

SPOJ Problem Set (classical)

1776. DNA Laboratory

Problem code: DNALAB

Having started to build his own DNA lab just recently, the evil doctor Frankenstein is not quite up to date yet. He wants to extract his DNA, enhance it somewhat and clone himself. He has already figured out how to extract DNA from some of his blood cells, but unfortunately reading off the DNA sequence means breaking the DNA into a number of short pieces and analyzing those first. Frankenstein has not quite understood how to put the pieces together to recover the original
sequence.

His pragmatic approach to the problem is to sneak into university and to kidnap a number of smart looking students. Not surprisingly, you are one of them, so you would better come up with a solution pretty fast.

You are given a list of strings over the alphabet A (for adenine), C (cytosine), G (guanine), and T (thymine), and your task is to find the shortest string (which is typically not listed) that contains all given strings as substrings. If there are several such strings of shortest length, find the smallest in alphabetical/lexicographical order.

Input
The fist line contains the number of scenarios. For each scenario, the first line contains the number n of strings with 1<=n<=15. Then these strings with 1 <= length <= 100 follow, one on each line, and they consist of the letters ‘A’, ‘C’, ‘G’, and ‘T’ only.

Output
The output for every scenario begins with a line containing “Scenario #i:”, where i is the number of the scenario starting at 1. Then print a single line containing the shortest (and smallest) string as described above. Terminate the output for the scenario with a blank line.

Sample Input
1
2
TGCACA
CAT

Sample Output

Scenario #1:
TGCACAT

Added by:	Andrés Leonardo Rojas Duarte
Date:	2007-09-15
Time limit:	12s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	TUD Programming Contest 2004

SPOJ Problem Set (classical)

1784. IOICamp Sequence

Problem code: ICAMPSEQ

Input

The first line: N (N ≤ 100000).
Following are N lines: the i-th line contains four real numbers A_i, B_i, C_i, D_i. (-10⁹ ≤ A_i, B_i, C_i, D_i ≤ 10⁹)

Output

Only one line is the maximum of F(i, j).
(The result takes exactly 3 decimal places)

Example

Input:
2
1.0 1.0 2.0 0.5
1.0 1.0 0.5 2.0


Output:
3.000

Added by:	Nghia Nguyen Hoang
Date:	2007-09-18
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	IOICamp and Ms. Thanh Vy Hua Le

SPOJ Problem Set (classical)

1785. Code

Problem code: CODE

KEY Inc., the leading company in security hardware, has developed a new kind of safe. To unlock it, you don't need a key but you are required to enter the correct n-digit code on a keypad (as if this were something new!). There are several models available, from toy safes for children (with a 2-digit code) to the military version (with a 6-digit code).

The safe will open as soon as the last digit of the correct code is entered. There is no "enter" key. When you enter more than n digits, only the last n digits are significant. For example (in the 4-digit version), if the correct code is 4567, and you plan to enter the digit sequence 1234567890, the door will open as soon as you press the 7 key.

The software to create this effect is rather simple. In the n-digit version the safe is always in one of 10^n-1 internal states. The current state of the safe simply represents the last n-1 digits that have been entered. One of these states (in the example above, state 456) is marked as the unlocked state. If the safe is in the unlocked state and then the right key (in the example above, 7) is pressed, the door opens. Otherwise the safe shifts to the corresponding new state. For example, if the safe is in state 456 and then you press 8, the safe goes into state 568.

A trivial strategy to open the safe is to enter all possible codes one after the other. In the worst case, however, this will require n * 10ⁿ keystrokes. By choosing a good digit sequence it is possible to open the safe in at most 10ⁿ + n - 1 keystrokes. All you have to do is to find a digit sequence that contains all n-digit sequences exactly once. KEY Inc. claims that for the military version (n=6) the fastest computers available today would need billions of years to find such a sequence - but apparently they don't know what some programmers are capable of...

Input Specification

The input contains several test cases. Every test case is specified by an integer n. You may assume that 1<=n<=6. The last test case is followed by a zero.

Output Specification

For each test case specified by n output a line containing a sequence of 10ⁿ + n - 1 digits that contains each n-digit sequence exactly once.

Sample Input

1
2
0

Sample Output

0123456789
00102030405060708091121314151617181922324252627282933435363738394454647484955657585966768697787988990

Added by:	Wanderley Guimarăes
Date:	2007-09-19
Time limit:	2s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS
Resource:	University of Ulm Local Contest 2004

SPOJ Problem Set (classical)

1786. In Danger

Problem code: DANGER

Flavius Josephus and 40 fellow rebels were trapped by the Romans. His companions preferred suicide to surrender, so they decided to form a circle and to kill every third person and to proceed around the circle until no one was left. Josephus was not excited by the idea of killing himself, so he calculated the position to be the last man standing (and then he did not commit suicide since nobody could watch).

We will consider a variant of this "game" where every second person leaves. And of course there will be more than 41 persons, for we now have computers. You have to calculate the safe position. Be careful because we might apply your program to calculate the winner of this contest!

Input Specification

The input contains several test cases. Each specifies a number n, denoting the number of persons participating in the game. To make things more difficult, it always has the format "xyez" with the following semantics: when n is written down in decimal notation, its first digit is x, its second digit is y, and then follow z zeros. Whereas 0<=x,y<=9, the number of zeros is 0<=z<=6. You may assume that n>0. The last test case is followed by the string 00e0.

Output Specification

For each test case generate a line containing the position of the person who survives. Assume that the participants have serial numbers from 1 to n and that the counting starts with person 1, i.e., the first person leaving is the one with number 2. For example, if there are 5 persons in the circle, counting proceeds as 2, 4, 1, 5 and person 3 is staying alive.

Sample Input

05e0
01e1
42e0
66e6
00e0

Sample Output

Added by:	Wanderley Guimarăes
Date:	2007-09-19
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS
Resource:	University of Ulm Local Contest 2004

SPOJ Problem Set (classical)

1787. Run Length Encoding

Problem code: ENCONDIN

Your task is to write a program that performs a simple form of run-length encoding, as described by the rules below.

Any sequence of between 2 to 9 identical characters is encoded by two characters. The first character is the length of the sequence, represented by one of the characters 2 through 9. The second character is the value of the repeated character. A sequence of more than 9 identical characters is dealt with by first encoding 9 characters, then the remaining ones.

Any sequence of characters that does not contain consecutive repetitions of any characters is represented by a 1 character followed by the sequence of characters, terminated with another 1. If a 1 appears as part of the sequence, it is escaped with a 1, thus two 1 characters are output.

Input Specification

The input consists of letters (both upper- and lower-case), digits, spaces, and punctuation. Every line is terminated with a newline character and no other characters appear in the input.

Output Specification

Each line in the input is encoded separately as described above. The newline at the end of each line is not encoded, but is passed directly to the output.

Sample Input

AAAAAABCCCC
12344

Sample Output

6A1B14C
11123124

Added by:	Wanderley Guimarăes
Date:	2007-09-19
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS
Resource:	University of Ulm Local Contest 2004

SPOJ Problem Set ()

1788. Fractan

Problem code: FRACTAN

To play the "fraction game" corresponding to a given list f₁, f₂, ..., f_k of fractions and starting integer N, you repeatedly multiply the integer you have at any stage (initially N) by the earliest f_i in the list for which the answer is integral. Whenever there is no such f_i, the game stops.

Formally, we define a sequence by S₀=N, and S_j+1=f_iS_j, if for 1<=i<=k, the number f_iS_j is an integer but the numbers f₁S_j, ..., f_i-1S_j are not.

For example, if we have the list of eight fractions f₁=170/39, f₂=19/13, f₃=13/17, f₄=69/95, f₅=19/23, f₆=1/19, f₇=13/7, f₈=1/3, and start with N=21, we produce the (finite) sequence (21,39,170,130,190,138,114,6,2). In general, the sequence may be infinite.

Given a fraction list and a starting integer calculate a part of the defined sequence. Actually, we are interested only in the powers of 2 that appear in the sequence.

Input Specification

The input contains several test cases. Every test case starts with three integers m, N, k. You may assume that 1<=m<=40, 1<=N<=1000, and 1<=k<=100. Then follow k fractions f₁, ..., f_k. For each fraction, first its numerator is given, followed by its denominator. You may assume that both are positive integers less than 1000 and their greatest common divisor is 1. The last test case is followed by a zero.

Output Specification

For each test case output on a line m numbers e₁, ..., e_m, separated by one space character, such that 2^e₁, ..., 2^e_k are the first m numbers in the defined sequence that are powers of 2. You may assume that there are at least m powers of 2 among the first 7654321 elements of the sequence.

Sample Input

1 21 8 170 39 19 13 13 17 69 95 19 23 1 19 13 7 1 3
20 2 14 17 91 78 85 19 51 23 38 29 33 77 29 95 23 77 19 1 17 11 13 13 11 15 2 1 7 55 1
0

Sample Output

1
1 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67

Added by:	Wanderley Guimarăes
Date:	2007-09-19
Time limit:	2s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	University of Ulm Local Contest 2004

SPOJ Problem Set (classical)

1789. Huffman´s Greed

Problem code: GREEDULM

In the following we define the basic terminology of trees. A tree is defined inductively: It has a root which is either an external node (a leaf), or an internal node having a sequence of trees as its children. An internal node is also called the parent of the roots of its child trees. The level of a node in a tree is defined inductively: The root has level 0, and the level of a node is 1 more than the level of its parent node.

Every internal node of a binary tree has precisely two children, its left sub-tree and its right sub-tree. Every internal node of a labelled binary tree is additionally marked with a string, its label. A binary search tree is a labelled binary tree where every internal node t satisfies the following condition: All labels of nodes in the left sub-tree of t are less than the label of t which is, in turn, less than all labels of nodes in the right sub-tree of t. For this condition, we assume lexicographic, i.e., alphabetic order on the strings.

An inorder traversal of a tree is defined recursively: A leaf is just visited, and for an internal node first its left sub-tree is traversed inorder, then the node itself is visited, finally its right sub-tree is traversed inorder. It follows that an inorder traversal of a binary search tree yields the labels in lexicographic order. Note that binary search trees whose shapes differ may nevertheless yield the same sequence of strings while being traversed inorder.

When a given string s is looked for in a binary search tree, we compare s to the label l of the root. We are done if s=l, otherwise if s<l we continue to search in the left sub-tree, and if s>l in the right sub-tree. If a leaf is reached, we know that s is not in the tree.

The number of comparisons performed in such a search procedure depends on s and the actual shape of the search tree. Therefore, there is an interest in constructing binary search trees that store a given sequence of strings but provide as efficient access as possible. Of course, we don't know in advance which strings will be looked up in the tree, so we need to make some assumptions.

Let n be the number of strings that are to be stored in the binary search tree. Let K₁,...,K_n be these strings in lexicographic order. Let p₁,...,p_n and q₀,...,q_n be 2n+1 non-negative real numbers such that ∑_i=1..n p_i + ∑_i=0..n q_i = 1. The interpretation of these numbers is:

p_i = probability that the search argument s is K_i.
q_i = probability that s lies (lexicographically) strictly between K_i and K_i+1.

By convention, q₀ is the probability that s is less than K₁, and q_n is the probability that s is greater than K_n. We want to find a binary search tree containing nodes with labels K₁,...,K_n that minimises the expected number of comparisons in the search, namely

cost = ∑_i=1..n p_i*(1 + level of internal node K_i) + ∑_i=0..n q_i*(level of leaf between K_i and K_i+1).

The leaf between K_i and K_i+1 is that leaf reached in the search for a string s that lies (lexicographically) strictly between K_i and K_i+1. Adhere to the convention stated above for the border cases.

The following figure illustrates the first test case of the sample input. It shows the two possible binary search trees, the probabilities and the associated costs.

Input Specification

The input contains several test cases. Every test case starts with an integer n. You may assume that 1<=n<=200. Then follow 2n+1 non-negative integers denoting frequencies. Let s be the sum of all frequencies. You may assume that 1<=s<=1000000. The probabilities p₁,...,p_n and q₀,...,q_n are calculated in this order by dividing the frequencies by s. The last test case is followed by a zero.

Output Specification

For each test case devise a binary search tree whose cost is minimal for the specified probabilities. Output the integer cost*s for such a tree.

Sample Input

2
20 15 15 25 25
35
142 35 58 5 20 5 10 9 15 23 129 4 52 5 38 18 9 7 2 4 266 93 5 18 18 27 5 10 11 180 4 32 21 3 21
0 55 27 36 85 31 58 3 334 0 98 27 113 89 180 0 62 12 0 37 0 3 64 70 0 277 0 0 0 170 0 18 76 27 3 29
0

Sample Output

160
13637

Added by:	Wanderley Guimarăes
Date:	2007-09-19
Time limit:	2s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS
Resource:	University of Ulm Local Contest 2004

SPOJ Problem Set ()

1790. Binary Search Heap Construction

Problem code: HEAPULM

Read the statement of problem G for the definitions concerning trees. In the following we define the basic terminology of heaps. A heap is a tree whose internal nodes have each assigned a priority (a number) such that the priority of each internal node is less than the priority of its parent. As a consequence, the root has the greatest priority in the tree, which is one of the reasons why heaps can be used for the implementation of priority queues and for sorting.

A binary tree in which each internal node has both a label and a priority, and which is both a binary search tree with respect to the labels and a heap with respect to the priorities, is called a treap. Your task is, given a set of label-priority-pairs, with unique labels and unique priorities, to construct a treap containing this data.

Input Specification

The input contains several test cases. Every test case starts with an integer n. You may assume that 1<=n<=50000. Then follow n pairs of strings and numbers l₁/p₁,...,l_n/p_n denoting the label and priority of each node. The strings are non-empty and composed of lower-case letters, and the numbers are non-negative integers. The last test case is followed by a zero.

Output Specification

For each test case output on a single line a treap that contains the specified nodes. A treap is printed as (<left sub-treap><label>/<priority><right sub-treap>). The sub-treaps are printed recursively, and omitted if leafs.

Sample Input

7 a/7 b/6 c/5 d/4 e/3 f/2 g/1
7 a/1 b/2 c/3 d/4 e/5 f/6 g/7
7 a/3 b/6 c/4 d/7 e/2 f/5 g/1
0

Sample Output

(a/7(b/6(c/5(d/4(e/3(f/2(g/1)))))))
(((((((a/1)b/2)c/3)d/4)e/5)f/6)g/7)
(((a/3)b/6(c/4))d/7((e/2)f/5(g/1)))

Added by:	Wanderley Guimarăes
Date:	2007-09-19
Time limit:	4s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	University of Ulm Local Contest 2004

SPOJ Problem Set (classical)

1793. Text Generater II

Problem code: GEN2

HL, HJ and FGD set problem for ZMY everyday. The title of each problem bores them very much. The title is a string which consists only lower case letters. It's length is L, and, of course, the title must contain their names(hl, hj, fgd) as consecutive substrings.More apparently, N evil consecutive substrings should not appear in the title. Any string satisfying the two conditions above is OK.

The task ZMY is to do today is: if they give ZMY 8 problems every week, and the title of each problem should not be repeated, how many (complete) weeks can they set problems?

Input

Multiple test cases.Input terminates by EOF.

For each test case:

The first line contains two space-seperated integers L(0<=L<=10⁹) and N(0<=N<=20). N lines follow, each contains a string (contains only lowercase letters), which is evil.You can assume the total length of the N evil strings is no more than 20.

Output

For each test case output one line contains the answer modudo 1000.

Example

Input:
10 1
zmy

Output:
245

Added by:	[Trichromatic] XilinX
Date:	2007-09-20
Time limit:	7s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	description by Blue Mary; standard program and test data by g201513

SPOJ Problem Set (classical)

1794. Greedy Hydra II

Problem code: DRAGON2

The problem description is the same as the problem DRAGON.

Input

The first line contains 3 integers N(1<=N<=3000),M(2<=M<=N),K(1<=K<=N), separated by single spaces. The N fruits are numbered 1..N, and the biggest fruit is always numbered 1. N-1 lines follow, each contains 3 integers i,j,k separated by spaces denoted that there is a branch between fruit i(1<=i<=N) and fruit j(1<=j<=N) and the weight of illness of this branch is k(0<=k<=100000).

Output

Output one line contains a single integer denoted the minimum weight of illness of the hydra. If we can't divide the fruit into M groups, output "-1"(without quotes).

Example

Blue Mary's Note: some new test cases were added on Dec.7, 2007.

Added by:	[Trichromatic] XilinX
Date:	2007-09-20
Time limit:	0.5s-1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	description by Blue Mary; standard program and test data by lcosvse

SPOJ Problem Set (classical)

1797. Cardsharper

Problem code: CARD

Zenek is a well known (at least in Byteotia) card-sharper. He spent most of his best years practicing one card shuffle with his deck of n cards, which for simplicity we will call 1,2,...,n. Unfortunately, it turns out that knowing this one card shuffle a is not enough to earn a good living. To become rich and famous Zenek needs to know k shuffles c₁,...,c_k. As he doesn't have enough time to learn all of them, he decided to learn only one shuffle b so that using both a and b he will be able to perform as many of c_i as it is possible.

Each shuffle is described by n numbers t₁,t₂,...,t_n. Such description means that after performing shuffle, card that was originally at position i will be at position t_i.

Task

Find shuffle b maximizing number of shuffles that can be performed.

Input

First line contains n (2≤n≤52). Second line contains n numbers a₁,a₂,...,a_n describing shuffle that Zenek already knows.Third line contains k (2≤k≤6). i-th of the next k lines contains description of c_i.

Output

First line contains description of the shuffle b that Zenek shoud learn. i-th of the next k lines contains:

-1 when it is not possible to perform c_i using only a and b
m,r₁,r₂,...,r_m (0≤m≤500000, 0≤r_i≤10⁶) meaning that applying a r₁ times, then b r₂ times, then a r₃ times and so on is the same as applying shuffle c_i once.

Examples

Input

Output

2 1 3 4 5
3 4 1 1
0
9 1 1 3 1 4 1 1 1 1

Input

Output

Added by:	Pawel Gawrychowski
Date:	2007-09-20
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Fajne Zawody Informatyczne

SPOJ Problem Set (classical)

1798. Assistance Required

Problem code: ASSIST

After the 1997/1998 Southwestern European Regional Contest (which was held in Ulm) a large contest party took place. The organization team invented a special mode of choosing those participants that were to assist with washing the dirty dishes. The contestants would line up in a queue, one behind the other. Each contestant got a number starting with 2 for the first one, 3 for the second one, 4 for the third one, and so on, consecutively.

The first contestant in the queue was asked for his number (which was 2). He was freed from the washing up and could party on, but every second contestant behind him had to go to the kitchen (those with numbers 4, 6, 8, etc). Then the next contestant in the remaining queue had to tell his number. He answered 3 and was freed from assisting, but every third contestant behind him was to help (those with numbers 9, 15, 21, etc). The next in the remaining queue had number 5 and was free, but every fifth contestant behind him was selected (those with numbers 19, 35, 49, etc). The next had number 7 and was free, but every seventh behind him had to assist, and so on.

Let us call the number of a contestant who does not need to assist with washing up a lucky number. Continuing the selection scheme, the lucky numbers are the ordered sequence 2, 3, 5, 7, 11, 13, 17, etc. Find out the lucky numbers to be prepared for the next contest party.

Input Specification

The input contains several test cases. Each test case consists of an integer n. You may assume that 1<=n<=3000. A zero follows the input for the last test case.

Output Specification

For each test case specified by n output on a single line the n-th lucky number.

Sample Input

Sample Output

Added by:	Wanderley Guimarăes
Date:	2007-09-21
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS
Resource:	University of Ulm Local Contest 2003

SPOJ Problem Set (classical)

1799. The Bottom of a Graph

Problem code: BOTTOM

We will use the following (standard) definitions from graph theory. Let V be a nonempty and finite set, its elements being called vertices (or nodes). Let E be a subset of the Cartesian product V×V, its elements being called edges. Then G=(V,E) is called a directed graph.

Let n be a positive integer, and let p=(e₁,...,e_n) be a sequence of length n of edges e_i∈ E such that e_i=(v_i,v_i+1) for a sequence of vertices (v₁,...,v_n+1). Then p is called a path from vertex v₁ to vertex v_n+1 in G and we say that v_n+1 is reachable from v₁, writing (v₁→v_n+1).

Here are some new definitions. A node v in a graph G=(V,E) is called a sink, if for every node w in G that is reachable from v, v is also reachable from w. The bottom of a graph is the subset of all nodes that are sinks, i.e., bottom(G)={v∈V|∀w∈V:(v→w)⇒(w→v)}. You have to calculate the bottom of certain graphs.

Input Specification

The input contains several test cases, each of which corresponds to a directed graph G. Each test case starts with an integer number v, denoting the number of vertices of G=(V,E), where the vertices will be identified by the integer numbers in the set V={1,...,v}. You may assume that 1<=v<=5000. That is followed by a non-negative integer e and, thereafter, e pairs of vertex identifiers v₁,w₁,...,v_e,w_e with the meaning that (v_i,w_i)∈E. There are no edges other than specified by these pairs. The last test case is followed by a zero.

Output Specification

For each test case output the bottom of the specified graph on a single line. To this end, print the numbers of all nodes that are sinks in sorted order separated by a single space character. If the bottom is empty, print an empty line.

Sample Input

3 3
1 3 2 3 3 1
2 1
1 2
0

Sample Output

1 3
2

Added by:	Wanderley Guimarăes
Date:	2007-09-21
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS
Resource:	University of Ulm Local Contest 2003

SPOJ Problem Set (classical)

1800. Fixed Partition Contest Management

Problem code: CONTEST

A technique used in early programming contest strategies involved partitioning the available intellectual capacity of a team into a number of members with each member having a fixed amount of intelligence, different members potentially having different amounts. The sum of the brightness of all members equals the total intellectual capacity of the team.

Given a set of problems, it was the task of the team to assign the problems to different team members, so that they could be solved concurrently. This was made difficult due to the fact that the solution time of a problem might depend on the amount of intelligence available to it. Every problem has a minimum intelligence requirement, but if assigned to a brighter member its solution time might increase or decrease.

In this task, you have to determine optimal assignments of problems to team members. Your program is given the intellectual capacities of the team members available for the solution of problems, and for each problem a description of how its solution time depends on the amount of intelligence available to it. Your program has to find the solution schedule of the problems that minimizes the average solution time for the problems. A solution schedule is an assignment of problems to team members and times, such that no two problems use the same member at the same time, and no problem is assigned to a team member with less brightness than its minimum requirement. The solution time of the problem is the difference between the time when the problem was submitted to be solved (which is the start of the contest at time zero for all problems in this task), and the time that the problem is solved.

Input Specification

The input data will contain multiple test cases. Each test case begins with a line containing a pair of integers m and n. The number m specifies the number of team members (1 <= m <= 3), and n specifies the number of problems to be solved (1 <= n <= 10).

The next line contains m positive integers giving the intelligence amounts of the m team members. Following this are n lines, describing the time-brightness tradeoffs for each of the n problems. Each line starts with a positive integer k (k <= 10), followed by k pairs of positive integers s₁,t₁,s₂,t₂,...,s_k,t_k that satisfy s_i < s_i+1 for 1 <= i < k. The minimum intelligence requirement of the problem is s₁, i.e. it cannot be solved by a member with less intellectual capacity than this number. If the problem is solved by a team member with brightness s, where s_i <= s < s_i+1 for some i, then its solution time will be t_i. Finally, if the problem is solved by a team member with intellectual capacity s_k or more, then its execution time will be t_k.

A pair of zeroes will follow the input for the last test case.

You may assume that each problem will be solved in exactly the time specified for the given brightness, regardless of the number of other problems being solved by other team members at the same time. No problem will have an intelligence requirement larger than that of the brightest team member.

Output Specification

For each test case, first display the case number (starting with 1 and increasing sequentially). Then print the minimum average solution time for the set of problems with two digits to the right of the decimal point. Follow this by the description of a solution schedule that achieves this average solution time. Display one line for each problem, in the order they were given in the input, that identifies the problem number, the member used to solve it (numbered in the order given in the input), the time when the member started to solve the problem, and the time when the problem was solved. Follow the format shown in the sample output, and print a blank line after each test case.

Sample Input

2 4
40 60
1 35 4
1 20 3
1 40 10
1 60 7
3 5
10 20 30
2 10 50 12 30
2 10 100 20 25
1 25 19
1 19 41
2 10 18 30 42
0 0

Sample Output

Case 1
Average solution time = 7.75
Problem 1 is solved by member 2 from 0 to 4
Problem 2 is solved by member 1 from 0 to 3
Problem 3 is solved by member 1 from 3 to 13
Problem 4 is solved by member 2 from 4 to 11

Case 2
Average solution time = 35.40
Problem 1 is solved by member 3 from 19 to 49
Problem 2 is solved by member 2 from 0 to 25
Problem 3 is solved by member 3 from 0 to 19
Problem 4 is solved by member 2 from 25 to 66
Problem 5 is solved by member 1 from 0 to 18

Added by:	Wanderley Guimarăes
Date:	2007-09-21
Time limit:	2s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS
Resource:	University of Ulm Local Contest 2003

SPOJ Problem Set (classical)

1801. Drink, on Ice

Problem code: DRINK

A good drink is always served on ice. That said, the amount of ice is what makes the difference. If it is too much, the drink will be well cooled, however, this is a bit of fraud as there could be less ice (and more Vodka for example). On the other hand, if there is too little ice the drink is warm which is unacceptable. You are to help the bartender, of course neither with mixing nor drinking, but with calculating the expected outcome of such mixtures.

To make things easier, we assume that pure water is mixed with ice in a closed system, i.e., there is no problem with the outside temperature or the warming of the bottle, etc. Therefore, after a some time has passed, the system may be regarded as balanced (there is no further change in temperature and no more melting or freezing). Your job is to calculate the final temperature of this balanced system and the amount of ice and water in this equilibrium state.

As you know from physics, it takes 4.19 Joule to heat one gram of water one Kelvin, whereas it takes 2.09 Joule if it is ice. We define the capacities c_w = 4.19 J/(g*K) and c_i = 2.09 J/(g*K). Melting one gram of ice takes 335 Joule, where the temperature remains constant at zero. We define the constant e_m = 335 J/g. The total thermal energy of the ice and the water before the experiment is equal to the thermal energy of the final mixture.

The figure below shows the energy of one gram of ice, ice-water-mixture, or water, where the temperature is measured relative to -30 degrees Celsius. The jump at 0 degrees represents the melting of ice to water. The amount of energy gained is proportional to the amount of ice already melted.

Input Specification

The input contains several test cases. Each test case consists of four real numbers m_w, m_i, t_w, t_i. The mass of water m_w and the mass of ice m_i are both non-negative, given in grams, and m_w + m_i > 0. The water temperature t_w and the ice temperature t_i follow, both given in degrees Celsius, and you may assume that -30 < t_i <= 0 <= t_w < 100. The last test case is followed by four zeroes.

Output Specification

For each test case output the amount of ice and water in grams and the final temperature of the mixture in degrees Celsius. All numbers must be rounded to one digit. Adhere to the sample output for the exact format to use.

Sample Input

100 20 50 -10 100 22 0 0 100 35 25 -10.5 10 90 25 -28 0 0 0 0

Sample Output

0.0 g of ice and 120.0 g of water at 27.5 C 22.0 g of ice and 100.0 g of water at 0.0 C 6.0 g of ice and 129.0 g of water at 0.0 C 100.0 g of ice and 0.0 g of water at -4.2 C

Added by:	Wanderley Guimarăes
Date:	2007-09-21
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS
Resource:	University of Ulm Local Contest 2003

SPOJ Problem Set (classical)

1802. Edge

Problem code: EDGE

For products that are wrapped in small packings it is necessary that the sheet of paper containing the directions for use is folded until its size becomes small enough. We assume that a sheet of paper is rectangular and only folded along lines parallel to its initially shorter edge. The act of folding along such a line, however, can be performed in two directions: either the surface on the top of the sheet is brought together, or the surface on its bottom. In both cases the two parts of the rectangle that are separated by the folding line are laid together neatly and we ignore any differences in thickness of the resulting folded sheet.

After several such folding steps have been performed we may unfold the sheet again and take a look at its longer edge holding the sheet so that it appears as a one-dimensional curve, actually a concatenation of line segments. If we move along this curve in a fixed direction we can classify every place where the sheet was folded as either type A meaning a clockwise turn or type V meaning a counter-clockwise turn. Given such a sequence of classifications, produce a drawing of the longer edge of the sheet assuming 90 degree turns at equidistant places.

Input Specification

The input contains several test cases, each on a separate line. Each line contains a nonempty string of characters A and V describing the longer edge of the sheet. You may assume that the length of the string is less than 200. The input file terminates immediately after the last test case.

Output Specification

For each test case generate a PostScript drawing of the edge with commands placed on separate lines. Start every drawing at the coordinates (300,420) with the command "300 420 moveto". The first turn occurs at (310,420) using the command "310 420 lineto". Continue with clockwise or counter-clockwise turns according to the input string, using a sequence of "x y lineto" commands with the appropriate coordinates. The turning points are separated at a distance of 10 units. Do not forget the end point of the edge and finish each test case by the commands stroke and showpage.

You may display such drawings with the gv PostScript interpreter, optionally after a conversion using the ps2ps utility.

Sample Input

V AVV

Sample Output

300 420 moveto 310 420 lineto 310 430 lineto stroke showpage 300 420 moveto 310 420 lineto 310 410 lineto 320 410 lineto 320 420 lineto stroke showpage

Added by:	Wanderley Guimarăes
Date:	2007-09-21
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS
Resource:	University of Ulm Local Contest 2003

SPOJ Problem Set (classical)

1803. Fold

Problem code: FOLD

Read the statement of problem E: Edge to understand how to fold a sheet of paper and how to interpret the input. We define a "stripe" to be a maximally large part of the sheet that has no folding line going through. Since the turns occur at equidistant places, all stripes are congruent.

In this problem you are given the description of the result of performing several folding steps as in problem E: Edge, i.e., in the unfolded state. Additionally, you know that the length of the sheet in its folded state is exactly the length of 1 stripe (again, we ignore thickness).

Find the minimum number of folding steps necessary to generate the described sheet from an initially flat sheet of paper. Note that performing a folding step may create more than one turn in the result because parts of the sheet already overlay due to previous folding steps. When a step is carried out, however, all overlaying parts of the sheet are affected, i.e., it is not allowed to fold, say, only the top three layers.

Finally, note that every result can be obtained by iterating through the turns in a fixed direction and performing a folding step at each turn, thereby accumulating a 1 stripe long stack of all stripes. If n is the number of turns in the input description, this procedure in fact requires n folding steps, which is not necessarily minimal as can be observed in the sample output.

Input Specification

Output Specification

For each test case print on a line the minimum number of folding steps required to produce the described sheet of paper.

Sample Input

V
AVV
AAVAAVVVAAV

Sample Output

1
2
4

Added by:	Wanderley Guimarăes
Date:	2007-09-21
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS
Resource:	University of Ulm Local Contest 2003

SPOJ Problem Set ()

1804. Genetic Code

Problem code: GENETIC

The connections between mathematics and biology are complicated. Most of the time they do not run along nice-looking links that merrily join at first glance, but they are abstract and not always easily established.

Lake Vostok - about 14000 square kilometers large, up to 650 meters deep, and covered by 3743 meters of ice - was recently discovered on the Antarctic continent. The lake remained under conditions of high pressure and no sunlight for several millions of years. It is believed that ordinary life has evolved to a more efficient form using a genetic code composed of only three bases (the current state of ignorance proclaims the four bases adenine, cytosine, guanine, and thymine). Until reasonable names are found, the three bases will be abbreviated as N, O, and P.

Moreover, the genome is single-stranded and directed, i.e., we may see it as a sequence over the alphabet {N,O,P}. Unless risking instability, it is necessary that the genome is a Thue-sequence, due to the Norwegian mathematician A. Thue (1863-1922). Define a subsegment of a sequence to be a connected subsequence, and call two subsegments adjacent if one follows immediately after the other in the sequence. A Thue-sequence is a sequence where no adjacent subsegments are equal. For example, NOPNO is and NOPNPNO is not a Thue-sequence, so that the first may be a genome whereas the second may not.

To be able to simulate experiments with the new genomes, you are asked to generate genomes of certain lengths.

Input Specification

The input contains several test cases. Each test case consists of an integer n. You may assume that 1<=n<=5000. The last test case is followed by a zero.

Output Specification

For each test case specified by n output on a single line any genome of length n. If no genome of length n exists, output a blank line instead.

Sample Input

Sample Output

N
NO
NONPNOPNPO
NONPNOPNPONOPNONPNOP

Added by:	Wanderley Guimarăes
Date:	2007-09-21
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	University of Ulm Local Contest 2003

SPOJ Problem Set (classical)

1805. Largest Rectangle in a Histogram

Problem code: HISTOGRA

A histogram is a polygon composed of a sequence of rectangles aligned at a common base line. The rectangles have equal widths but may have different heights. For example, the figure on the left shows the histogram that consists of rectangles with the heights 2, 1, 4, 5, 1, 3, 3, measured in units where 1 is the width of the rectangles:

Usually, histograms are used to represent discrete distributions, e.g., the frequencies of characters in texts. Note that the order of the rectangles, i.e., their heights, is important. Calculate the area of the largest rectangle in a histogram that is aligned at the common base line, too. The figure on the right shows the largest aligned rectangle for the depicted histogram.

Input Specification

The input contains several test cases. Each test case describes a histogram and starts with an integer n, denoting the number of rectangles it is composed of. You may assume that 1<=n<=100000. Then follow n integers h₁,...,h_n, where 0<=h_i<=1000000000. These numbers denote the heights of the rectangles of the histogram in left-to-right order. The width of each rectangle is 1. A zero follows the input for the last test case.

Output Specification

For each test case output on a single line the area of the largest rectangle in the specified histogram. Remember that this rectangle must be aligned at the common base line.

Sample Input

7 2 1 4 5 1 3 3
4 1000 1000 1000 1000
0

Sample Output

8
4000

Added by:	Wanderley Guimarăes
Date:	2007-09-21
Time limit:	3s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS
Resource:	University of Ulm Local Contest 2003

SPOJ Problem Set (classical)

1810. Nuclear Plants

Problem code: ORZ

The Great Plain of Algorithmia plays an extremely important role in the agriculture of the Bandulu Kingdom: this is the only place where barley (Hordeum vulgare), an essential ingredient of beer, can be produced. Unfortunately, it is not possible to grow barley on the full area of the plain, as several nuclear plants have recently been built, and you cannot grow barley near a nuclear plant (since you do not want to produce giant-size, aggressive, man-eating barley-mutants). Your task is to write a program that determines the size of the area that can be used for growing barley.

The Great Plain of Algorithmia is an n * m km² rectangle, the coordinates of the four corners being (0, 0),(0, m),(n, 0) and (n, m). There are two types of nuclear plants: small and large. You are not allowed to grow barley within 0.58km of a small nuclear plant or within 1.31km of a large nuclear plant.

Input

The input contains several blocks of test cases. Each block begins with a line containing four integers: 1 <= n, m <= 10000 describe the size of the plain, ks <= 100 is the number of small nuclear plants, and kl <= 100 is the number of large nuclear plants. The next ks lines describe the coordinates of the small nuclear plants, each line contains two integers 0 <= x <= n and 0 <= y <= m . The next kl lines describe the large nuclear plants in a similar fashion.

The input is terminated by a block with n = m = ks = kl = 0 .

Output

For each test case, you have to output a single line containing the area that can be used for growing barley. This number should be a real value with two digits of precision. To avoid rounding problems, we accept solutions with a maximum of 0.01(positive or negative) error.

Example

Time limit has been changed from 2 seconds to 5 seconds.

Added by:	[Trichromatic] XilinX
Date:	2007-09-23
Time limit:	5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	ACM Central European Programming Contest, Budapest 2005

SPOJ Problem Set (classical)

1811. Longest Common Substring

Problem code: LCS

A string is finite sequence of characters over a non-empty finite set Σ.

In this problem, Σ is the set of lowercase letters.

Substring, also called factor, is a consecutive sequence of characters occurrences at least once in a string.

Now your task is simple, for two given strings, find the length of the longest common substring of them.

Here common substring means a substring of two or more strings.

Input

The input contains exactly two lines, each line consists of no more than 250000 lowercase letters, representing a string.

Output

The length of the longest common substring. If such string doesn't exist, print "0" instead.

Example

Input:
alsdfkjfjkdsal
fdjskalajfkdsla

Output:
3

Notice: new testcases added

Added by:	Bin Jin
Date:	2007-09-24
Time limit:	2s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C++ 4.0.0-8

SPOJ Problem Set (classical)

1812. Longest Common Substring II

Problem code: LCS2

A string is finite sequence of characters over a non-empty finite set Σ.

In this problem, Σ is the set of lowercase letters.

Substring, also called factor, is a consecutive sequence of characters occurrences at least once in a string.

Now your task is a bit harder, for some given strings, find the length of the longest common substring of them.

Here common substring means a substring of two or more strings.

Input

The input contains at most 10 lines, each line consists of no more than 100000 lowercase letters, representing a string.

Output

The length of the longest common substring. If such string doesn't exist, print "0" instead.

Example

Input:
alsdfkjfjkdsal
fdjskalajfkdsla
aaaajfaaaa

Output:
2

Notice: new testcases added

Added by:	Bin Jin
Date:	2007-09-24
Time limit:	2s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C++ 4.0.0-8

SPOJ Problem Set (classical)

1815. Problems Collection (Volume X)

Problem code: WA

These ten problems come from Chinese National Olympiad in Mathematics - Province Contest.

Problem 1 Polynomial P(x)=x⁵+a₁x⁴+a₂x³+a₃x²+a₄x+a₅, and we know when k=1, 2, 3, 4, P(k)=2007*k. Calculate P(10)-P(-5).

Problem 2 The sum of 100 positive integers a₁, a₂, ..., a₁₀₀ is 2007. Calculate the maximum possible value of .

Problem 3 Calculate 100101102103104......498499500 modulo 126.

Problem 4 We define the sum of the first n numbers of geometric progression {a_n} S_n. Now we know S₇=7, S₁₄=2014. Calculate S₇*(S₂₁-S₁₄).

Problem 5 Calculate the sum of this kind of positive integers n(n>=4): n satisfies that n! can be written as the product of n-3 consecutive positive integers.

Problem 6 Two vertices of a square are on the line y=2x-17, while the other two are on the parabola y=x². Calculate the sum of two different possible values of the area of this square.

Problem 7 A, B, C, D are four fixed points in the space and they are not on the same plane. Calculate the number of different parallelepipeds, which satisfies that 4 vertices of the parallelepiped are A, B, C and D.

Problem 8 Polynomial x²-x-1 exactly divides Polynomial a₁x¹⁷+a₂x¹⁶+1. Calculate a₁*a₂.

Problem 9 Suppose x is an acute angle, calculate the minimum possible value of (sin x +cos x)/(sin x +tan x) + (tan x +cot x)/(cos x +tan x) + (sin x +cos x)/(cos x +cot x) + (tan x +cot x)/(sin x +cot x).

Problem 10 Suppose x⁴+y⁴+z⁴=m/n, x, y, z are all real numbers, satisfying x*y+y*z+z*x=1 and 5*(x+1/x)=12*(y+1/y)=13*(z+1/z); m, n are positive integers and their greatest common divisor is 1. Calculate m+n.

Input

There is no input.

Output

Ten lines, each contains a single integer denoted the answer to the correspoding problem.

Example

There is no example.

Links

If there is any problem, please contact me.

Added by:	[Trichromatic] XilinX
Date:	2007-09-27
Time limit:	1s
Source limit:	60B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	TEXT
Resource:	CMOP :)

SPOJ Problem Set (classical)

1825. Free tour II

Problem code: FTOUR2

After the success of 2nd anniversary (take a look at problem FTOUR for more details), this 3rd year, Travel Agent SPOJ goes on with another discount tour.

The tour will be held on ICPC island, a miraculous one on the Pacific Ocean. We list N places (indexed from 1 to N) where the visitors can have a trip. Each road connecting them has an interest value, and this value can be negative (if there is nothing interesting to view there). Simply, these N places along with the roads connecting them form a tree structure. We will choose two places as the departure and destination of the tour.

Since September is the festival season of local inhabitants, some places are extremely crowded (we call them crowded places). Therefore, the organizer of the excursion hopes the tour will visit at most K crowded places (too tiring to visit many of them) and of course, the total number of interesting value should be maximum.

Briefly, you are given a map of N places, an integer K, and M id numbers of crowded place. Please help us to find the optimal tour. Note that we can visit each place only once (or our customers easily feel bored), also the departure and destination places don't need to be different.

Input

There is exactly one case. First one line, containing 3 integers N K M, with 1 <= N <= 200000, 0 <= K <= M, 0 <= M <= N.

Next M lines, each line includes an id number of a crowded place.

The last (N - 1) lines describe (N - 1) two-way roads connected N places, form a b i, with a, b is the id of 2 places, and i is its interest value (-10000 <= i <= 10000).

Output

Only one number, the maximum total interest value we can obtain.

Example

Explanation

We choose 2 and 6 as the departure and destination place, so the tour will be 2 -> 3 -> 4 -> 5 -> 6, total interest value = 10 + (-2) + (-1) + 5 = 12

* Added some unofficial cases

Added by:	Thanh-Vy Hua
Date:	2007-09-28
Time limit:	1s-5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	Adapted from Preslav Le's problem, first used in Bulgarian OI 07

SPOJ Problem Set (classical)

1833. Sudoku

Problem code: SUDOKU2

Oh no! Bill just realized that the sudoku puzzle he had spent the last ten minutes trying to solve essentially was last week's puzzle, only rotated counterclockwise. How cheap! Couldn't the magazine afford to make a new one every week? Of course, he had no way of knowing about this before he started to solve it, as the holes to fill with digits were other than last week. Nevertheless, realizing that this week's puzzle was a simple derivative of last week's certainly took the fun out of solving the rest of it.

The sudoku board consists of 9×9 cells. These can be grouped into 3×3 regions of 3×3 cells each. Some of the cells are filled with a digit 1 through 9 while the rest of them are left empty. The aim of the game is to fill each empty cell with a digit 1...9 so that every row, every column and every region contains each of the numbers 1...9 exactly once. A proper sudoku puzzle always has exactly one solution.

Help Bill avoid unpleasant surprises by creating a program that checks whether an unsolved sudoku puzzle is in fact derived from an earlier puzzle by simple operations.

The allowed operations are:

Rotating the entire puzzle clockwise or counterclockwise.
Swapping two columns within a 3×9 column segment.
Swapping two rows within a 9×3 row segment.
Swapping entire row or column segments.
Applying a permutation f of the digits 1...9 to every cell (i.e. replace x by f(x) in every cell).

An operation is considered being performed on the sudoku solution (rather than on the unsolved puzzle) and always guarantees that if the board before the transformation was a solution to a sudoku puzzle, it still is afterwards.

Input

The input starts with the number of test cases 0 ≤ N ≤ 50 on a single line.

Then for every test case follow nine lines describing last week's puzzle solution, from top to bottom. Each line corresponds to a row in the puzzle and consists of nine digits (1...9), describing the contents of the cell from left to right.

Last week's solution is followed by nine lines describing this week's unsolved puzzle. Here, also, every line corresponds to a puzzle row and every digit (0...9) describes the contents of a cell. 0 indicates that the cell is empty. The rows are presented ordered from top to bottom, and within each row, the cells are ordered from left to right.

After every test case except the last one follows a blank line. Every unsolved puzzle is guaranteed to be uniquely solvable and last week's solution is always a proper sudoku solution. /p>

Output

For every test case, output Yes if the sudoku puzzle can be derived from the given solved puzzle using the allowed operations, or No if this is not possible.

Example

Added by:	Robin Nittka
Date:	2007-10-02
Time limit:	10s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	ACM ICPC NWERC 2006

SPOJ Problem Set ()

1835. The SetStack Computer

Problem code: SETSTACK

Background from Wikipedia: Set theory is a branch of mathematics created principally by the German mathematician Georg Cantor at the end of the 19th century. Initially controversial, set theory has come to play the role of a foundational theory in modern mathematics, in the sense of a theory invoked to justify assumptions made in mathematics concerning the existence of mathematical objects (such as numbers or functions) and their properties. Formal versions of set theory also have a foundational role to play as specifying a theoretical ideal of mathematical rigor in proofs.

Given this importance of sets, being the basis of mathematics, a set of eccentric theorist set off to construct a supercomputer operating on sets instead of numbers. The initial SetStack Alpha is under construction, and they need you to simulate it in order to verify the operation of the prototype.

The computer operates on a single stack of sets, which is initially empty. After each operation, the cardinality of the topmost set on the stack is output. The cardinality of a set S is denoted |S| and is the number of elements in S. The instruction set of the SetStack Alpha is PUSH, DUP, UNION, INTERSECT, and ADD}.

PUSH will push the empty set {} on the stack.
DUP will duplicate the topmost set (pop the stack, and then push that set on the stack twice).
UNION will pop the stack twice and then push the union of the two sets on the stack.
INTERSECT will pop the stack twice and then push the intersection of the two sets on the stack.
ADD will pop the stack twice, add the first set to the second one, and then push the resulting set on the stack.

For illustration purposes, assume that the topmost element of the stack is

A = { {}, {{}} },

and that the next one is

B = { {}, {{{}}} }.

For these sets, we have |A| = 2 and |B| = 2. Then:

UNION would result in the set { {}, {{}}, {{{}}} }. The output is 3.
INTERSECT would result in the set { {} }. The output is 1.
ADD would result in the set { {}, {{{}}}, {{},{{}}} }. The output is 3.

Input

An integer 0 ≤ T ≤ 5 on the first line gives the cardinality of the set of test cases. The first line of each test case contains the number of operations 0 ≤ N ≤ 2000. Then follow N lines each containing one of the five commands. It is guaranteed that the SetStack computer can execute all the commands in the sequence without ever popping an empty stack.

Output

For each operation specified in the input, there will be one line of output consisting of a single integer. This integer is the cardinality of the topmost element of the stack after the corresponding command has executed. After each test case there will be a line with *** (three asterisks).

Example

Input:
2
9
PUSH
DUP
ADD
PUSH
ADD
DUP
ADD
DUP
UNION
5
PUSH
PUSH
ADD
PUSH
INTERSECT

Output:
0
0
1
0
1
1
2
2
2
***
0
0
1
0
0
***

Added by:	Robin Nittka
Date:	2007-10-02
Time limit:	12s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	ACM ICPC NWERC 2006

SPOJ Problem Set (main)

1837. Pie

Problem code: PIE

My birthday is coming up and traditionally I'm serving pie. Not just one pie, no, I have a number N of them, of various tastes and of various sizes. F of my friends are coming to my party and each of them gets a piece of pie. This should be one piece of one pie, not several small pieces since that looks messy. This piece can be one whole pie though.

My friends are very annoying and if one of them gets a bigger piece than the others, they start complaining. Therefore all of them should get equally sized (but not necessarily equally shaped) pieces, even if this leads to some pie getting spoiled (which is better than spoiling the party). Of course, I want a piece of pie for myself too, and that piece should also be of the same size.

What is the largest possible piece size all of us can get? All the pies are cylindrical in shape and they all have the same height 1, but the radii of the pies can be different.

Input

One line with a positive integer: the number of test cases. Then for each test case:

One line with two integers N and F with 1 ≤ N, F ≤ 10000: the number of pies and the number of friends.
One line with N integers r_i with 1 ≤ r_i ≤ 10000: the radii of the pies.

Output

For each test case, output one line with the largest possible volume V such that me and my friends can all get a pie piece of size V. The answer should be given as a floating point number with an absolute error of at most 10^-3.

Example

Input:
3
3 3
4 3 3
1 24
5
10 5
1 4 2 3 4 5 6 5 4 2

Output:
25.1327
3.1416
50.2655

Added by:	Robin Nittka
Date:	2007-10-02
Time limit:	5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	ACM ICPC NWERC 2006

SPOJ Problem Set (classical)

1838. Ticket to Ride

Problem code: TICKET

Ticket to Ride is a board game for up to 5 players. The goal of the game is to set up train lines (and to thwart the opponents' attempts at setting up their train lines). At the beginning of play, each player is assigned four train lines. A player may choose to discard as many of these four assignments as she likes. Each assignment has a score, corresponding to its difficulty (so, typically, a train line between e.g. Stockholm and Tokyo would be worth more than a train line between e.g. Stockholm and Utrecht). At the end of the game, each player gets points for the assignments that they have successfully completed, and penalty points for the assignments that they have failed to complete.

An assignment consists of a pair of cities that are to be connected by a series of shorter railway routes. A route can be claimed (for a certain cost associated with the route), but things are complicated by the fact that there is only a limited number of routes, and once a player claims a route, none of the other players can claim it. A player has successfully set up a train line between two cities if there is a path between the two cities using only routes that have been claimed by this player. For simplicity, we will ignore all additional aspects of the game (including the actual process of claiming routes and additional ways to score points).

For instance, if your assignment is to connect Stockholm and Amsterdam in the Figure above, you would probably want to claim the routes between Stockholm and Copenhagen, and between Copenhagen and Amsterdam. But if another player manages to claim the route between Copenhagen and Stockholm before you, your train line would have to use some other routes, e.g. by going to Copenhagen via Oslo.

In this problem, we will consider the rather bold strategy of trying to complete all four assignments (typically, this will be quite hard). As a preliminary assessment of the difficulty of achieving this, we would like to calculate the minimum cost of setting up all four lines assuming that none of the other players interfere with our plans. Your job is to write a program to determine this minimum cost.

Input

The input consists of several (at most 20) games to be analyzed. Each game starts with two integers 1 ≤ n ≤ 30, 0 ≤ m ≤ 1000, giving the number of cities and railway routes in the map, respectively. Then follow n lines, giving the names of the n cities. City names are at most 20 characters long and consist solely of lower case letters ('a'-'z').

After this follow m lines, each containing the names of two different cities and an integer 1 ≤ c ≤ 10000, indicating that there is a railway route with cost c between the two cities. Note that there may be several railway routes between the same pair of cities. You may assume that it is always possible to set up a train line from any city to any other city.

Finally, there will be four lines, each containing the names of two cities, giving the four train line assignments.

The input is terminated by a case where n = m = 0. This case should not be processed.

Output

For each game, output a single line containing a single integer, the minimum possible cost to set up all four train lines.

Example

Input:
10 15
stockholm
amsterdam
london
berlin
copenhagen
oslo
helsinki
dublin
reykjavik
brussels
oslo stockholm 415
stockholm helsinki 396
oslo london 1153
oslo copenhagen 485
stockholm copenhagen 522
copenhagen berlin 354
copenhagen amsterdam 622
helsinki berlin 1107
london amsterdam 356
berlin amsterdam 575
london dublin 463
reykjavik dublin 1498
reykjavik oslo 1748
london brussels 318
brussels amsterdam 173
stockholm amsterdam
oslo london
reykjavik dublin
brussels helsinki
2 1
first
second
first second 10
first first
first first
second first
first first
0 0

Output:
3907
10

Added by:	Robin Nittka
Date:	2007-10-02
Time limit:	20s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	ACM ICPC NWERC 2006

SPOJ Problem Set ()

1839. The Bookcase

Problem code: BOOKCASE

No wonder the old bookcase caved under the massive piles of books Tom had stacked on it. He had better build a new one, this time large enough to hold all of his books. Tom finds it practical to have the books close at hand when he works at his desk. Therefore, he is imagining a compact solution with the bookcase standing on the back of the desk. Obviously, this would put some restrictions on the size of the bookcase, it should preferably be as small as possible. In addition, Tom would like the bookcase to have exactly three shelves for aesthetical reasons.

Wondering how small his bookcase could be, he models the problem as follows. He measures the height h_i and thickness t_i of each book i and he seeks a partition of the books in three non-empty sets S₁, S₂, S₃ such that

is minimized, i.e. the area of the bookcase as seen when standing in front of it (the depth needed is obviously the largest width of all his books, regardless of the partition). Note that this formula does not give the exact area of the bookcase, since the actual shelves cause a small additional height, and the sides cause a small additional width. For simplicity, we will ignore this small discrepancy.

Thinking a moment on the problem, Tom realizes he will need a computer program to do the job.

Input

The input begins with a positive number on a line of its own telling the number of test cases (at most 20). For each test case there is one line containing a single positive integer N, 3 ≤ N ≤ 70 giving the number of books. Then N lines follow each containing two positive integers h_i, t_i, satisfying 150 ≤ h_i ≤ 300 and 5 ≤ t_i ≤ 30, the height and thickness of book i respectively, in millimeters.

Output

For each test case, output one line containing the minimum area (height times width) of a three-shelf bookcase capable of holding all the books, expressed in square millimeters.

Example

Added by:	Robin Nittka
Date:	2007-10-02
Time limit:	40s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 n SCALA SED TCL
Resource:	ACM ICPC NWERC 2006

SPOJ Problem Set (classical)

1840. Printer Queue

Problem code: PQUEUE

The only printer in the computer science students' union is experiencing an extremely heavy workload. Sometimes there are a hundred jobs in the printer queue and you may have to wait for hours to get a single page of output.

Because some jobs are more important than others, the Hacker General has invented and implemented a simple priority system for the print job queue. Now, each job is assigned a priority between 1 and 9 (with 9 being the highest priority, and 1 being the lowest), and the printer operates as follows.

The first job J in queue is taken from the queue.
If there is some job in the queue with a higher priority than job J, then move J to the end of the queue without printing it.
Otherwise, print job J (and do not put it back in the queue).

In this way, all those important muffin recipes that the Hacker General is printing get printed very quickly. Of course, those annoying term papers that others are printing may have to wait for quite some time to get printed, but that's life.

Your problem with the new policy is that it has become quite tricky to determine when your print job will actually be completed. You decide to write a program to figure this out. The program will be given the current queue (as a list of priorities) as well as the position of your job in the queue, and must then calculate how long it will take until your job is printed, assuming that no additional jobs will be added to the queue. To simplify matters, we assume that printing a job always takes exactly one minute, and that adding and removing jobs from the queue is instantaneous.

Input

One line with a positive integer: the number of test cases (at most 100). Then for each test case:

One line with two integers n and m, where n is the number of jobs in the queue (1 ≤ n ≤ 100) and m is the position of your job (0 ≤ m ≤ n-1). The first position in the queue is number 0, the second is number 1, and so on.
One line with n integers in the range 1 to 9, giving the priorities of the jobs in the queue. The first integer gives the priority of the first job, the second integer the priority of the second job, and so on.

Output

For each test case, print one line with a single integer; the number of minutes until your job is completely printed, assuming that no additional print jobs will arrive.

Example

Input:
3
1 0
5
4 2
1 2 3 4
6 0
1 1 9 1 1 1

Output:
1
2
5

Added by:	Robin Nittka
Date:	2007-10-02
Time limit:	2s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	ACM ICPC NWERC 2006

SPOJ Problem Set (classical)

1841. Prime Path

Problem code: PPATH

The ministers of the cabinet were quite upset by the message from the Chief of Security stating that they would all have to change the four-digit room numbers on their offices.
— It is a matter of security to change such things every now and then, to keep the enemy in the dark.
— But look, I have chosen my number 1033 for good reasons. I am the Prime minister, you know!
— I know, so therefore your new number 8179 is also a prime. You will just have to paste four new digits over the four old ones on your office door.
— No, it's not that simple. Suppose that I change the first digit to an 8, then the number will read 8033 which is not a prime!
— I see, being the prime minister you cannot stand having a non-prime number on your door even for a few seconds.
— Correct! So I must invent a scheme for going from 1033 to 8179 by a path of prime numbers where only one digit is changed from one prime to the next prime.

Now, the minister of finance, who had been eavesdropping, intervened.
— No unnecessary expenditure, please! I happen to know that the price of a digit is one pound.
— Hmm, in that case I need a computer program to minimize the cost. You don't know some very cheap software gurus, do you?
— In fact, I do. You see, there is this programming contest going on...

Help the prime minister to find the cheapest prime path between any two given four-digit primes! The first digit must be nonzero, of course. Here is a solution in the case above.

The cost of this solution is 6 pounds. Note that the digit 1 which got pasted over in step 2 can not be reused in the last step – a new 1 must be purchased.

Input

One line with a positive number: the number of test cases (at most 100). Then for each test case, one line with two numbers separated by a blank. Both numbers are four-digit primes (without leading zeros).

Output

One line for each case, either with a number stating the minimal cost or containing the word Impossible.

Example

Input:
3
1033 8179
1373 8017
1033 1033

Output:
6
7
0

Added by:	Robin Nittka
Date:	2007-10-02
Time limit:	3s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	ACM ICPC NWERC 2006

SPOJ Problem Set (classical)

1842. Lineland Airport

Problem code: LINELAND

Lineland is a strange country. As the name suggests, it's shape (as seen from above) is just a straight line, rather than some two-dimensional shape. The landscape along this line is very mountainous, something which occasionally leads to some problems. One such problem now occurs: in this modern era the king wants to build an airport to stimulate the country's economy. Unfortunately, it's impossible for airplanes to land on steep airstrips, so a horizontal piece of land is needed. To accommodate for the larger airplanes, this strip needs to have length at least L.

Over the years, the inhabitants of Lineland have become very proficient in flattening pieces of land. Given a piece a land, they can remove rock quickly. They don't want to add rock for that may lead to an unstable landing strip. To minimize the amount of effort, however, they want to remove the least amount of rock necessary to reach their goal: a flat piece of land of length L. What is this minimum amount? Because of the low-dimensional nature of Lineland, the amount of rock that needs to be removed is measured as the total area of land above the place where the landing strip is placed, rather than the volume (so in the Figure below, the amount of land removed is given by the lightly shaded area).

Input

One line with a positive number: the number of test cases (at most 25). Then for each test case:

One line with an integer N, 2 ≤ N ≤ 500, the number of points, and an integer L, 1 ≤ L ≤ 10000, the necessary length to flatten.
N lines with two integers x_i and y_i with 0 ≤ x_i, y_i ≤ 10000 describing the landscape of Lineland. The x_i are in (strictly) ascending order. At position x_i the height of the landscape is x_i. Between two x_i the landscape has constant slope. (So the landscape is piecewise linear). The difference between x_N and x₁ is greater than or equal to L.

Output

For each test case, output one line with the minimum amount of rock which must be removed in order to build the airport. The answer should be given as a floating point number with an absolute error of at most 10^-3.

Example

Input:
4
3 5
0 2
4 2
14 0
4 3
0 2
2 0
4 0
5 3
3 10
10 2
30 2
35 7
2 777
222 333
4444 5555

Output:
0.9000
0.3750
0.0000
373362.4867

Added by:	Robin Nittka
Date:	2007-10-02
Time limit:	20s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	ACM ICPC NWERC 2006

SPOJ Problem Set (classical)

1843. Leonardo Notebook

Problem code: LEONARDO

— I just bought Leonardo's secret notebook!
Rare object collector Stan Ucker was really agitated but his friend, special investigator Sarah Keptic was unimpressed.
— How do you know it is genuine?
— Oh, it must be, at that price. And it is written in the da Vinci code.
Sarah browsed a few of the pages. It was obvious to her that the code was a substitution cipher, where each letter of the alphabet had been substituted by another letter.
— Leonardo would have written the plain-text and left it to his assistant to encrypt, she said. And he must have supplied the substitution alphabet to be used. If we are lucky, we can find it on the back cover!
She turned up the last page and, lo and behold, there was a single line of all 26 letters of the alphabet:

QWERTYUIOPASDFGHJKLZXCVBNM

— This may be Leonardo's instructions meaning that each A in the plain-text was to be replaced by Q, each B with W, etcetera. Let us see...
To their disappointment, they soon saw that this could not be the substitution that was used in the book. Suddenly, Stan brightened.
— Maybe Leonardo really wrote the substitution alphabet on the last page, and by mistake his assistant coded that line as he had coded the rest of the book. So the line we have here is the result of applying some permutation TWICE to the ordinary alphabet!
Sarah took out her laptop computer and coded fiercely for a few minutes. Then she turned to Stan with a sympathetic expression.
— No, that couldn't be it. I am afraid that you have been duped again, my friend. In all probability, the book is a fake.
Write a program that takes a permutation of the English alphabet as input and decides if it may be the result of performing some permutation twice.

Input

The input begins with a positive number on a line of its own telling the number of test cases (at most 500). Then for each test case there is one line containing a permutation of the 26 capital letters of the English alphabet.

Output

For each test case, output one line containing Yes if the given permutation can result from applying some permutation twice on the original alphabet string ABC...XYZ, otherwise output No.

Example

Input:
2
QWERTYUIOPASDFGHJKLZXCVBNM
ABCDEFGHIJKLMNOPQRSTUVWXYZ

Output:
No
Yes

Added by:	Robin Nittka
Date:	2007-10-02
Time limit:	2s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	ACM ICPC NWERC 2006

SPOJ Problem Set (classical)

1845. Mice and Maze

Problem code: MICEMAZE

A set of laboratory mice is being trained to escape a maze. The maze is made up of cells, and each cell is connected to some other cells. However, there are obstacles in the passage between cells and therefore there is a time penalty to overcome the passage Also, some passages allow mice to go one-way, but not the other way round.

Suppose that all mice are now trained and, when placed in an arbitrary cell in the maze, take a path that leads them to the exit cell in minimum time.

We are going to conduct the following experiment: a mouse is placed in each cell of the maze and a count-down timer is started. When the timer stops we count the number of mice out of the maze.

Problem

Write a program that, given a description of the maze and the time limit, predicts the number of mice that will exit the maze. Assume that there are no bottlenecks is the maze, i.e. that all cells have room for an arbitrary number of mice.

Input

The maze cells are numbered $1,2,\ldots,N$ , where is the total number of cells. You can assume that $N\leq 100$ .

The first three input lines contain , the number of cells in the maze, , the number of the exit cell, and the starting value for the count-down timer (in some arbitrary time unit).

The fourth line contains the number of connections in the maze, and is followed by lines, each specifying a connection with three integer numbers: two cell numbers and (in the range $1,\ldots,N$ ) and the number of time units it takes to travel from to .

Notice that each connection is one-way, i.e., the mice can't travel from to unless there is another line specifying that passage. Notice also that the time required to travel in each direction might be different.

Output

The output consists of a single line with the number of mice that reached the exit cell in at most time units.

Example

Added by:	Robin Nittka
Date:	2007-10-04
Time limit:	2s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	ACM ICPC -- SWERC 2001

SPOJ Problem Set (classical)

1846. Project File Dependencies

Problem code: PFDEP

Project managers, such as the UNIX utility make, are used to maintain large software projects made up from many components. Users write a project file specifying which components (called tasks) depend on others and the project manager can automatically update the components in the correct order.

Problem

Write a program that reads a project file and outputs the order in which the tasks should be performed.

Input

For simplicity we represent each task by an integer number from $1,2,\ldots,N$ (where is the total number of tasks). The first line of input specifies the number of tasks and the number of rules, such that $N \leq 100,\; M\leq 100$ .

The rest of the input consists of rules, one in each line, specifying dependencies using the following syntax:

...

This rule means that task number

depends on

tasks $T_1, T_2, \ldots T_k$ (we say that task

is the target and $T_1\ldots T_k$ are dependents).

Note that tasks numbers are separated by single spaces and that rules end with a newline. Rules can appear in any order, but each task can appear as target only once.

Your program can assume that there are no circular dependencies in the rules, i.e. no task depends directly or indirectly on itself.

Output

The output should be a single line with the permutation of the tasks $1\ldots N$ to be performed, ordered by dependencies (i.e. no task should appear before others that it depends on).

To avoid ambiguity in the output, tasks that do not depend on each other should be ordered by their number (lower numbers first).

Example

Input:
5 4
3 2 1 5
2 2 5 3
4 1 3
5 1 1

Output:
1 5 3 2 4

Added by:	Robin Nittka
Date:	2007-10-04
Time limit:	2s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	ACM ICPC -- SWERC 2001

SPOJ Problem Set (classical)

1847. No Change

Problem code: NOCHANGE

Though it might be hard to imagine, the inhabitants of a small country Additivia do not know of such thing as change, which probably has to do with them not knowing subtraction either. When they buy something, they always need to have the exact amount of addollars, their currency. The only other option, but not a really attractive one, is over-paying.

Professor Adem, one of the Additivian mathematicians came up with an algorithm for keeping a balanced portfolio. The idea is the following. Suppose you have more coins of value than coins of value . In this case you should try to spend at least as many coins of value as those of value on any buy you make. Of course spending too many coins is not a good idea either, but to make the algorithm simpler professor Adem decided to ignore the problem. The algorithm became an instant hit and professor Adem is now designing a kind of ``electronic portfolio'' with built-in Adem's algorithm. All he needs now is a software for these machines, that will decide whether a given amount of addollars can be paid using a given set of coins according to the rules of Adem's algorithm. Needless to say, you are his chosen programmer for the task.

Problem

Write a program that reads the description of a set of coins and an amount of addollars to be paid, and determines whether you can pay that amount according to Professor Adem's rules.

Input

The input starts with the amount of addollars to be paid , where $1\le x \le 100 000$ . The number of different coin values follows, where $1 \le k \le 5$ . The values of the coins $v_1,\ldots,v_k$ follow, where $1 \le v_i \le 10 000$ .

Notice that the order among coin values is significant: you need to spend at least as many coins of value as coins of value , at least as many coins of value as those of value , and so on. You may assume that you have a sufficiently large number of coins of each value.

Output

Your program should output for each test case either a single word ``YES'', if the given amount can be paid according to the rules, or a single word ``NO'' otherwise.

Example

Input:
13 3 9 2 1
Output:
NO

Added by:	Robin Nittka
Date:	2007-10-04
Time limit:	5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	ACM ICPC -- SWERC 2001

SPOJ Problem Set ()

1865. Making Waves

Problem code: MKWAVES

Suppose we know a signal is generated by the function x sin (f₁t) sin (f₂t). F1 and f2 are two unique frequencies, each having an integral value in the range 400 to 600 Hz (Hz = cycles per second), and t represents time. In this problem, you will be given N samples of this function at equally-spaced time intervals corresponding to t = 1/N, t = 2/N, and so forth. From these samples, you are to determine f1 and f2.

For example, suppose f1 = 400 Hz, f2 = 500 Hz, and N = 100. The first sample, at time t = 1/100 sec, is equal to sin(400 0.01) sin(500 0.01) sin(4) sin(5) 0.156912 . Similarly, the second sample, at time t = 2/100 sec, is equal to sin(400 0.02) sin(500 0.02) sin(8) sin(10) 0.312821.

Input

There will be multiple cases to consider. Each case begins with an integer N, no larger than 1000, that specifies the number of signal samples. The next N data items are real numbers representing the signal samples at time 1/N sec, 2/N sec, and so forth. A single integer 0 follows the last case.

The number of samples for each case is guaranteed to be sufficient to allow the correct result to be obtained.

Output

For each input case, display a single line that is formatted like this:

Case 1, f1 = 400, f2 = 500

Example

Input:
100
0.156912 0.312821 0.466731 0.617657 0.764638 0.906737 1.04305 1.17271
1.29489 1.40883 1.51381 1.60917 1.69432 1.76873 1.83195 1.8836 1.92338
1.95106 1.96649 1.96962 1.96045 1.93908 1.9057 1.86055 1.80396 1.73634
1.65816 1.56997 1.47237 1.36603 1.25166 1.13003 1.00196 0.868307 0.729943
0.587785 0.442764 0.295823 0.147918 1.68756e-010 -0.146981 -0.292088
-0.434403 -0.573031 -0.707107 -0.835801 -0.958325 -1.07394 -1.18195
-1.28171 -1.37266 -1.45428 -1.52611 -1.58779 -1.63898 -1.67947 -1.70907
-1.7277 -1.73535 -1.73205 -1.71795 -1.69323 -1.65816 -1.61308 -1.55838
-1.49452 -1.42201 -1.34141 -1.25334 -1.15846 -1.05745 -0.951057 -0.840028
-0.725146 -0.607206 -0.487017 -0.365392 -0.243145 -0.121082 -2.75143e-010
0.119322 0.236125 0.34968 0.459289 0.564288 0.664055 0.758014 0.845635
0.926438 1 1.06595 1.12398 1.17384 1.21533 1.24833 1.27276 1.28862
1.29596 1.29489 1.28558

0

Output:
Case 1, f1 = 400, f2 = 500

Added by:	Camilo Andrés Varela León
Date:	2007-10-07
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	North Central North America Regional Programming Contest - 2003

SPOJ Problem Set (classical)

1866. Making Pals

Problem code: MKPALS

A palindrome is a sequence that is the same when read forward or backward. For example, “pop” is a palindrome, as are “Poor Dan is in a droop” (ignoring spaces and case), and “12321”.

In this problem, you are to find the “cheapest” way to transform a sequence of decimal digits into a palindrome. There are only two types of modifications you may make to the sequence, but each of these may be repeated as many times as necessary. You may delete a digit from either end of the sequence, or you may add a digit to either end of the sequence. Each of these operations incurs a “cost” of 1. For each input sequence, determine the smallest cost of transforming the sequence into a palindrome, and the length of the resulting palindrome. If two palindromes can be produced with the same cost, the length of the longer palindrome (the one with more digits) is to be reported.

For example, suppose the initial sequence was “911”. This can be transformed into a palindrome by deleting the leading “9” (yielding “11”) or by adding an additional “9” to the right end of the sequence (yielding “9119”). Since both of these transformations have a cost of 1, and the second transformation yields a longer palindrome, it is this one which would be reported as your result.

Note that the particular palindrome produced by the cheapest sequence of transformations is not necessarily unique, but since you are not required to report the resulting palindrome, any of these will suffice.

Input

There will be multiple cases to consider. Each case has a single line of input that contains one or more decimal digits followed by the end of line. The maximum number of digits in a sequence will be 6. The last case is followed by an empty line (that is, only an end of line).

Output

For each input case, display the case number (1, 2, …), the input sequence, the cost of the cheapest transformation, and the length of the resulting palindrome. Your output should follow the format shown in the examples below.

Example

Input:
911
9118
11234
<-- This line is blank

Output:
Case 1, sequence = 911, cost = 1, length = 4
Case 2, sequence = 9118, cost = 2, length = 4
Case 3, sequence = 11234, cost = 3, length = 8

Added by:	Camilo Andrés Varela León
Date:	2007-10-07
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	North Central North America Regional Programming Contest - 2003

SPOJ Problem Set ()

1868. Making Money

Problem code: MKMONEY

A trick sometimes used by parents to teach their children the value of money is to give then a penny – just a penny! – and the promise that for each day they don’t spend it, the parent will double it. All students of computing know that long before a month has elapsed without spending a cent, the parents will not likely be able to make good on their promise.

100-percent compound daily interest on an investment is, of course, unattainable in normal financial dealings, but we are all continually reminded of the power of compound interest, even with the relatively low interest rates available today.

But exactly how much money can be made with compound interest? Assume, for example, an initial investment of $100.00 (US or Canadian ☺), an annual interest rate of 6.00 percent, and that interest is compounded monthly. That is, the interest earned during the preceding month is added to the principal at the end of the month. (For our purposes, we’ll assume a month is exactly 1/12th of a year.)

At the end of the first month, the money will have earned 0.5 percent interest (1/12th of 6.00 percent), or $0.50. This is added to the $100.00 invested, so that during the next month, interest is paid on $100.50. During the next month another 0.5 percent interest is earned, which is exactly $0.5025. We will assume that the bank, being conservative, will not pay any interest less than $0.01, so our investment is credited with an additional $0.50 at the end of the second month, for a whopping total of $101.00. Continuing in the same manner, at the end of 12 months our investment will total $106.12, $0.12 more than simple 6.00 percent interest for a year with no compounding.

Given an amount P to be invested for a year with I percent interest, compounded C times during the year at equal intervals, what is total return on the investment?

Input

There will be multiple cases to consider. The input for each case is a single line containing the initial investment amount, P, given in dollars and cents (but no fractional cents, and no larger than $100,000.00), the annual interest rate (I) given as a real number with two fractional digits representing a percentage, greater than zero but less than 100, and the number of compounding intervals per year (C), an integer between 1 and 365. The last case will be followed by a line containing “0.00 0.00 0”.

Output

For each input case, display the case number (1, 2, …), the initial investment (P), the annual interest rate (I), the number of compounding intervals per year(C), and the value of the investment at the end of a year. Your output should follow the format shown in the examples below.

Example

Input:
100.00 6.00 1
100.00 6.00 12
1000.00 6.00 12
0.00 0.00 0

Output:
Case 1. $100.00 at 6.00% APR compounded 1 times yields $106.00
Case 2. $100.00 at 6.00% APR compounded 12 times yields $106.12
Case 3. $1000.00 at 6.00% APR compounded 12 times yields $1061.63

Added by:	Camilo Andrés Varela León
Date:	2007-10-07
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	North Central North America Regional Programming Contest - 2003

SPOJ Problem Set ()

1869. Making Mountains Out Of Molehills

Problem code: MKMOOM

A macro processor is a symbol processing program. It takes a stream of characters as its input, and produces a stream of characters as its output. A “macro” is similar to ordinary function in that it has a definition, and when invoked, that definition is applied to the argument(s) to yield the result. In this problem, you will develop a simple macro processor.

A “macro call” consists of a name and a list of arguments, separated by commas. The name is preceded by '[' (a left bracket) and the last argument is followed by ']' (a right bracket). For example, “[doit,to,it]” calls the macro named “doit” with two arguments, “to” and “it”. “[random]” calls the macro named “random” with no arguments.

Before a macro can be called, it must be defined by associating its name with a symbol string. This definition string may contain the special constructions “$1” through “$9” to reference the first through the ninth macro parameters. “$0” references the macro’s name itself. When the macro is called, these constructions are literally replaced by the values of the parameters. For example, suppose the definition string for the macro named “321” was “$3-$2-$1”. The macro call “[321,This,is,fun]” would yield the output “fun-is-This”. A macro call can appear anywhere. For example, the macro call “[321,[321,A,B,C],D,E]” would yield the output “E-D-C-B-A”.

Input enclosed in '<' and '>' prevents the evaluation of the text enclosed, allowing special characters like '[', ']', ',' and '$' to be used in other than their usual contexts. Thus the macro call “[321,<$>,<[>,<,>]” would yield “,-[-$”.

Macros are defined using the predefined macro named “def”, which has two arguments. The first argument is the name of the macro being defined, and the second argument is the defining symbol string for the macro. The “321” macro definition is “[def,321,<$3-$2-$1>]”. Note that the definition is enclosed in '<' and '>' to prevent “$1”, “$2”, and “$3” from being interpreted as parameter references to def. The def macro produces no output. Naturally, the def macro isn’t defined using def, but is treated specially by the implementation.

Processing

The input stream is processed character by character and copied to the output until a macro call is encountered, or the input is exhausted (which terminates processing). A macro call is evaluated as described below, with the result (if any) copied to the output.

The macro name and the parameters are evaluated in sequence from left to right. This may require evaluating additional macro calls, which must be processed recursively.
When the argument list is complete (that is, when the closing ']' is encountered) the definition of the macro being called is scanned in the same manner as the original input stream except that occurrences of “$0”, “$1”, and so forth are replaced literally by the corresponding arguments. The result of the macro call is the symbol stream produced by this scan.
When the macro call is completed, the macro name and the arguments are discarded, and processing resumes at the point where it was interrupted by the macro call.

Limits and Caveats

Macro names and arguments will contain no more than 32 characters each. The defining string for a macro will contain no more than 100 characters. Macros will never be defined more than once (that is, the same macro name will not be used more than once as the first argument to “def”). Macro calls will always provide the correct number of arguments. Character case is significant in comparisons. All input characters, including end of line characters, are to be processed through the macro processor. No output line will contain more than 80 characters, including the end of line character. The input is guaranteed to be correct.

Input

There will be multiple cases to consider. The input for each case begins with a line containing a single integer between 1 and 10, that specifies the number of lines of text immediately following that will be used as input to the macro processor. None of these lines will contain more than 80 characters, so the input to the macro processor will contain at most 810 characters. The last case will be followed by a line containing the integer 0.

Output

For each input case, display the case number (1, 2, …), a line containing 79 hyphens, the output from the macro processor, another line containing 79 hyphens, and a blank line.

In the sample input shown below, assume that the last visible character on each line is immediately followed by the end of line character. Blank lines in the expected output are shown here as **BLANK** for clarity, but these should actually be totally blank in your output.

Example

Input:
1
This is just copied (including end of line).
1
[def,321,<$3-$2-$1>][321,This,is,fun]
1
[def,321,<$3-$2-$1>][321,[321,A,B,C],D,E]
1
[def,321,<$3-$2-$1>][321,This,is,fun][321,[321,A,B,C],D,E]
3
[def,321,<$3-$2-$1>]
[321,This,is,fun]
[321,[321,A,B,C],D,E]
3
[def,A,<$1[B]$2>]
[def,B,*B*]
[A,1,2]
2
[def,#,<[-]$1[-]$2[-]$3[-]>][def,-,<$0>][def,DEF,def][[DEF],X,THIS IS X]
[X][#,DEF,#,X]
0

Output:
Case 1
-------------------------------------------------------------------------------
This is just copied (including end of line).
-------------------------------------------------------------------------------
**BLANK**
Case 2
-------------------------------------------------------------------------------
fun-is-This
-------------------------------------------------------------------------------
**BLANK**
Case 3
-------------------------------------------------------------------------------
E-D-C-B-A
-------------------------------------------------------------------------------
**BLANK**
Case 4
-------------------------------------------------------------------------------
fun-is-ThisE-D-C-B-A
-------------------------------------------------------------------------------
**BLANK**
Case 5
-------------------------------------------------------------------------------
**BLANK**
fun-is-This
E-D-C-B-A
-------------------------------------------------------------------------------
**BLANK**
Case 6
-------------------------------------------------------------------------------
**BLANK**
**BLANK**
1*B*2
-------------------------------------------------------------------------------
**BLANK**
Case 7
-------------------------------------------------------------------------------
**BLANK**
THIS IS X-DEF-#-X-
-------------------------------------------------------------------------------
**BLANK**

Added by:	Camilo Andrés Varela León
Date:	2007-10-07
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	North Central North America Regional Programming Contest - 2003

SPOJ Problem Set (classical)

1870. Making Labels

Problem code: MKLABELS

Trees comes in many varieties other than the popular binary tree. In general, a tree is a connected acyclic graph. That is, it consists of some number of vertices N (which we’ll assume is at least one in this problem), and N – 1 edges, each of which connects a pair of vertices.

A “labeled tree” is a tree in which each vertex has been given a “label.” For simplicity, let us assume these labels are the integers 1 through N. In how many different ways may a tree with N vertices be labeled? By “different” we mean that no rearrangement of two trees with the same number of vertices with different labeling will be identical. (Note that although we commonly associate data with each vertex, and identify one vertex as the root of the tree, that’s not significant in this problem.)

Let’s consider some examples. The figure below shows all possible arrangements of trees with N = 1, 2, 3, 4, or 5 vertices. The number shown below each tree is the number of different ways in which the vertices in each tree can be labeled.

Clearly a tree with only one vertex can be labeled in only one way – by assigning the label “1” to the single vertex. A tree with two vertices can also be labeled in only one way. For example, although the two trees shown on the left below appear to be different, the first can be easily transformed into the second. (Imagine the edges are strings, so the vertices can be easily repositioned without losing their connectivity.)

There are, however, three possible ways to label the vertices in a 3-vertex tree, as shown on the right above. No matter how you rearrange the labeled vertices in any of the three trees, you cannot produce any of the other labeled trees.

In a similar manner, the various arrangements of four vertices in a tree yield a total of 16 possible labelings – 12 for the four vertices “in a row,” and 4 for the other configuration. There are three possible arrangements of the vertices in a tree with N = 5, with a total of 125 possible

Input

There will be multiple cases to consider. The input for each case is an integer N specifying the number of vertices in a tree, which will always be between 1 and 10. The last case will be followed by a zero.

Output

For each input case, display the case number (1, 2, …), the input value of N, and the number of different ways in which a tree with N vertices may be labeled. Use the format shown in the examples below.

Example

Input:
2
3
4
5
0

Output:
Case 1, N = 2, # of different labelings = 1
Case 2, N = 3, # of different labelings = 3
Case 3, N = 4, # of different labelings = 16
Case 4, N = 5, # of different labelings = 125

Added by:	Camilo Andrés Varela León
Date:	2007-10-07
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	North Central North America Regional Programming Contest - 2003

SPOJ Problem Set (classical)

1871. Making A Budget

Problem code: MKBUDGET

A company uses temporary employees (“temps”) to handle its varying workloads. By doing so, it avoids having to pay for benefits normally provided to its permanent employees. However, the company must pay an employment agency a fixed fee for each temp they hire, as well as paying the temp a fixed amount of severance pay when they are terminated – in addition, of course, to the monthly salary each temp receives. The company has a good understanding of when it needs temporary workers, and how many such workers it will require each month. Depending on the fee paid to the employment agency, the temporary worker’s salary, and the severance pay, it may make sense to retain an unneeded worker for one or more months if it’s known that they will be needed again in the future.

Let’s consider an example. Suppose we know that in March the company will need 10 temps, in April they’ll need 9, and in May they’ll need 11. Suppose a temp earns $500 per month, that the employment agency receives $400 for each temp hired, and $600 is paid as severance to each temp that is terminated. If the company employs just the minimum number of temps required, then their payments will be as follows (we ignore the cost of terminating all employees at the end of the last month):

The total cost to the company is $20,400. But suppose they did not terminate the unneeded temp at the end of March, but just let that person remain employed. They would then save $400 in employment agency fees (since they’d need to hire just one additional temp for May), $600 in severance pay, and only have to pay the temp worker $500, for an overall savings of $500.

In this problem you are given, as input, the number of months for which the company is to plan its temp worker budget, the cost of hiring and firing a temp worker, the temp worker’s monthly salary, and the required minimum number of workers needed each month. You are to determine the minimum cost to the company to have at least the required minimum number of workers on hand each month. Assume there are no temporary workers on hand before the first month, and that the cost of terminating the workers at the end of the last month is not to be included in the cost. You may assume that the planning interval will be no longer than 24 months, and the hiring cost, severance pay, and monthly salary for each temp worker is greater than zero.

Input

There will be multiple cases to consider. The input for each case begins with an integer N, the number of months for which planning is required (never larger than 24). This is followed by three integers giving the cost of hiring a worker, the worker’s monthly salary, and the severance pay for a terminated worker. Finally there will appear N integers giving the required minimum number of workers needed in each month. The last case will be followed by a zero.

Output

For each input case, display the case number (1, 2, …) and the minimum cost to the company. Use the format shown in the examples below.

Example

Input:
3 400 500 600 10 9 11
8 400 600 600 11 9 10 14 9 9 13 15
0

Output:
Case 1, cost = $19900
Case 2, cost = $66600

Added by:	Camilo Andrés Varela León
Date:	2007-10-07
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	North Central North America Regional Programming Contest - 2003

SPOJ Problem Set ()

1873. Accumulate Cargo

Problem code: ACARGO

A cargo shipment containing N (1 <= N <= 10⁵) boxes, has just arrived and it requires some regrouping. All the cargo is currently placed on a long circular conveyor belt of length L metres (1 <= L <= 10⁹), which you can control and perform the following operations.

Rotate the wheel clock wise or anti-clockwise (free of cost).
Hold the cargo at some point and not let it move, while the belt is rolling. This causes the cargo behind it to come closer to this cargo by one step. Any consecutive sequence of cargo is grouped together and called as a luggage. The aim of the program is to group all cargo as a single luggage. Now the cost of this holding operation for one second is equal to the weight of the luggage that is held fixed. Also please note that you can hold the luggage only at ends of the luggage and never at inbetween points.

Each unit of cargo weighs exactly one Kg. The conveyor belt rotates at a speed of one meters per second.
This cost function directly reflects the human effort required to group the cargo. Workers would be happy if you can write a program that prints the minimal required effort to group the cargo, assuming an intelligent sequence of operations.

Input Format:
The input file consists of multiple testcases.
The first line of each testcase contains two integers, N and L.
The following N lines contain one integer each specifying the position of the i^th cargo on the belt. The positions will be between 0 & L-1.
Input terminates with a line containing N=0 and L=0 which must not be processed.

Output Format:
For each testcase print one integer in a single line, which is the minimal required cost for grouping all the cargo into a single luggage.

Sample Input:

Sample Output:

1
0
10

NOTE: Please use 64-bit integers.

Added by:	Prasanna
Date:	2007-10-08
Time limit:	1s-10s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 n SCALA SED TCL
Resource:	NITT ACM ICPC Local Contest 2007 [Idea from a Topcoder problem]

SPOJ Problem Set (classical)

1874. Burrows Wheeler Precompression

Problem code: BWHEELER

The Burrows-Wheeler transform (BWT, also called block-sorting compression), is an algorithm used in data compression techniques such as bzip2. It was invented by Michael Burrows and David Wheeler.

When a character string is transformed by the BWT, none of its characters change value. The transformation permutes the order of the characters. If the original string had several substrings that occurred often, then the transformed string will have several places where a single character is repeated multiple times in a row. This is useful for compression, since it tends to be easy to compress a string that has runs of repeated characters by techniques such as move-to-front transform and run-length encoding.

For example, the string:

SIX.MIXED.PIXIES.SIFT.SIXTY.PIXIE.DUST.BOXES

could be transformed into this string, which is easier to compress because it has many repeated characters:

 TEXYDST.E.IXIXIXXSSMPPS.B..E.S.EUSFXDIIOIIIT

Now the Burrows-Wheeler algorithm works as follows:

Given an input string S, eg: "abcba".

Find all rotations of S.

eg: "abcba", "bcbaa", "cbaab", "baabc", "aabcb"

Now sort the strings hence produced.

eg: "aabcb", "abcba", "baabc", "bcbaa", "cbaab"

Arrange the strings in a len(S) x len(S) grid.
```
aabcb
abcba
baabc
bcbaa
cbaab
```
Output the row number (1-based indexing) containing the original input string. Also output the strings formed by characters in the last column.
eg: 2 bacab

Now given the output of Burrows-Wheeler, can you recover the orginal string?

Input Format:
The input file consists of multiple testcases.
The first line of each testcase contains one integer, R, indicating the row number containing the original input string in the sorted matrix.
The second line of each testcase contains one string, Col, which is the last column of the grid. (1 <= len(Col) <= 1000)
Col contains only lowercase characters. 1 <= R <= len(Col).
Input terminates with a line containing R=0 which must not be processed.

Output Format:
Print the original input string to the burrow wheeler's algorithm.

Testdata:
30 testcases
Sample Input:

2
bacab
3
rwlb
11
baaabaaaabbbaba
0

Sample Output:

abcba
rbwl
baaabbbbaaaaaab

Added by:	Prasanna
Date:	2007-10-08
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	NITT ACM ICPC Local Contest 2007 [Wikipedia/General]

SPOJ Problem Set (classical)

1875. Cool Numbers

Problem code: COOLNUMS

Cool numbers are those, whose digits can be partitioned into two sets such that the sum of the digits in either sets are equal.
Example: 23450 is cool because 3+4+0 = 2+5; So is 91125;
The numbers 567, 34523 are not cool, since there is no such digit partition.

Write a program that prints the number of cool numbers in the inclusive range [A,B].

Input Format:
The input file consists of multiple testcases.
Each case contains one line containing two 32-bit unsigned integers A and B. (1 <= A <= B <= 4*10⁹).
Input terminates with a line containing two zeros and must not be processed.

Output Format:
For each testcase print a single line containing one integer saying the number of cool numbers between A and B, inclusive.

Sample Input:

1 11
12 20
1 20
3 100
6354 234363
123456789 234567891
0 0

Sample Output:

Test Data:
About 50 testcases.

Added by:	Prasanna
Date:	2007-10-08
Time limit:	30s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	NITT ACM ICPC Local Contest 2007 [Topcoder problem with Constraints raised]

SPOJ Problem Set (main)

1876. Dragon Curves

Problem code: DRAGONCU

Define r(s) to be the complement of the reverse of the binary string s. i.e. Reverse s and then convert all 1's to 0's and all 0's to 1's.
Further define a sequence of binary string as follow: s₀ = 1 and s_n = s_n-11r(s_n-1). i.e.
s₀ = 1
s₁ = 110
s₂ = 1101100
s₃ = 110110011100100
...

We then program a robot to move at a steady speed of 1 unit per second and make a right-angle turn according to the characters of s₁₀ after every unit of movement. At the kth turn, the robot turns to left if the kth character of s₁₀ is a 1, and to right otherwise. The figure below shows the whole path of the robot.

The robot is placed at the origin (the small circle) and face east originally. It ends up at the coordinates (-32,32) (the small spot) after 2048 seconds. The path of the robot is known as a dragon curve, a pretty well-known pattern of fractal.

If the robot is now programmed with input string s₃₀ (with identical initial conditions as above), it will keep moving and then stop after 2³¹ seconds. We want to know the location of the robot at any given time.

Input Format:
Input consists of multiple problem instances. Each instance consists of a single non-negative integer n, where n <= 10⁹. The input data is terminated by a "-1". There will be less than 5000 test cases.

Output Format:
For each input integer n, print out the location of the robot right after n second since the robot starts its journey with input string s₃₀. The location should be printed with the format "(x,y)" in a single line.

Sample Input:

Sample Output:

(1,0)
(1,1)
(0,1)
(-32,32)
(9648,-31504)

Added by:	Prasanna
Date:	2007-10-08
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	NITT ACM ICPC Local Contest 2007 [Tsinghua]

SPOJ Problem Set (main)

1877. Enrich my purse

Problem code: EPURSE

Jack plays this ball game for the first time in his club. Jack has a ball, which bounces with a width of W. Coins are arranged on a straight line at regular intervals. If the ball strikes the i-th coin, Jack gains money[i] (which could possibly be negative). Jack can take atmost B turns, to throw the ball. At each turn, jack can either throw the ball from left to right, or right to left, and choose which ball to start the knock out. If he chooses to knock out from ball i to the right, he will knock out i, i+W, i+2W, ...; Similarly if he chooses to knock out from right to left, starting from ball i he will knock out, i, i-W, i-2W, ...; Please note that once a ball is knocked out, it is removed and it's place contains a void. i.e., you cant gain money[i] for the same i twice.
Jack wants to maximise his money gained, by carefully choosing his turns. If there is more than one way to gain the same money, jack wishes to minimise the number of times he throws.

Input Format

The input file consists of multiple testcases.
The first line of each testcase contains three integers, W B N (1 <= N <= 100; W,B > 0)
The second line of each testcase contains N integers, denoting money[i]. (| money[i] | <= 10⁶)
Input terminates with a line containing three zeros which must not be processed.

Output Format

For each testcase print one line denoting the maximal money gained and the number of turns taken. Please see the sample output and stick to the output format.
"Case#id: Jack wins $X out of Y throws."
NOTE: You must spell the same way the sample output says. Extra spaces and case insensitivity can cause wrong answer responses.

Testdata:
100 testcases, Timelimit: 10s

Sample Input:

2 3 10
-1 3 2 5 1 -2 0 5 1 -3
2 3 14
-1 3 2 5 -5 -5 1 -2 0 5 -5 -5 1 -3
3 3 5
-1 -2 -3 -4 -5
1 2 6
-1 -1 10 10 -1 -1
0 0 0

Sample Output:

Case#1: Jack wins $15 out of 2 throws.
Case#2: Jack wins $10 out of 3 throws.
Case#3: Jack wins $0 out of 0 throws.
Case#4: Jack wins $18 out of 1 throws.

Output Explanation:
We present one of the optimal solutions. We number balls from 1 to N.
TestCase#1: [Jack takes only two throws, though he can take three]
Throw#1: From ball#3 towards right, 2 + 1 + 0 + 1 = 4
Throw#2: From ball#8 towards left, 5 + -2 + 5 + 3 = 11
TestCase#2:
Throw #1: From ball#3 towards left, 2 + -1 = 1
Throw #2: From ball#4 towards left, 5 + 3 = 8
Throw #3: From ball#13 towards right, 1 = 1
TestCase#3:
All numbers are negative. Jack takes no throws.

Added by:	Prasanna
Date:	2007-10-08
Time limit:	10s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	NITT ACM ICPC Local Contest 2007 [Self]

SPOJ Problem Set (classical)

1878. Farmers Cattle

Problem code: FCATTLE

Farmer john owns a single cow and he loves it a lot. The cow has a disease and is going to die. To survive, the cow needs medicine of a particular type each day. Let us say the cow needs medicine[i] to survive the i^th day. (medicine[i] will be terminated by -1, which is an unavailable medicine, and the cow has to invariably die that day).
To help the cow, john has decided to buy pastures of some medical value. Farmer sees a two-dimensional grid of pastures, each cell having exactly one medical herb. Now he needs to buy a sub-rectangular region of the grid, whose area cannot exceed A (A > 1). With this region the farmer intends to feed his cow, as long as possible.

Input Format:
The input file consists of multiple testcases.
The first line of each testcase contains three integers, R, C and A.
The second line consists of sequence of integers describing medicine[i]. This list will be terminated by -1.
The next R lines contain C integers each, specifying the medicinal type of the herb in that cell. (1 <= R,C <= 200). All herbs are specified by non negative integers.
Input terminates with a line containing three zeros and must not be processed.

Output Format:
For each testcase print a single line containing 5 integers:
days r1 c1 r2 c2
(1 <= r1 <= r2 <= R, 1 <= c1 <= c2 <= C)

days is the number of days the cow survives. We wish to maximise this.
If there are more than one solutions print the one with minimal r1.
If there are more than one solutions still, print the one with minimal c1.
If there are more than one solutions still, print the one with minimal r2.
If there are more than one solutions still, print the one with minimal c2.

Sample Input:

3 4 6
12 30 12 100 22 -1
30 12 5 3
12 30 100 5
22 3 22 100
3 4 6
2 30 12 100 22 -1
30 12 5 3
12 30 100 5
22 3 22 100
3 4 6
12 30 12 100 22 -1
30 12 5 3
12 30 100 5
22 12 22 100
0 0 0

Sample Output:

4 1 1 2 3
0 1 1 1 1
5 1 2 3 3

Added by:	Prasanna
Date:	2007-10-08
Time limit:	5s-120s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	NITT ACM ICPC Local Contest 2007 [Self]

SPOJ Problem Set (classical)

1879. Game Time

Problem code: GAMETIME

Jack has got a new game of Super Mario recently. There are n castles in the game, and Princess Peach has been kidnapped by the King Koopa and enjailed in castle n - 1 (0-based). The King Koopa has Son Koopas, and the Son Koopas has Grandson Koopas, and the Grandson Koopas has Great-Grandson Koopas... The whole Koopa family is taking possession of these n castles, and there is exactly one Koopa in each castle and the King Koopa is in castle n - 1. Super Mario's task is to conquer these castles and save Princess Peach.

Each time, Super Mario can freely choose an unconquered castle and go in to fight with the Koopa. Super Mario has time T[i] to conquer castle i and beat the Koopa in it. If Super Mario fails to conquer the castle or fails to do that within the time limit, the game is over. Otherwise, the defeated Koopa will go to seek the Father Koopa for help. If any Koopa has two or more Son Koopas beaten by Super Mario, he will get angry. Super Mario has to go to the castle of the angry Koopa and beat him immediately; otherwise the Princess Peach will be killed. If castle n - 1 is conquered and King Koopa is defeated, the game will also end, but with triumph and Princess Peach saved.

Jack loves this game a lot, but he has to prepare for the upcoming ACM/ICPC. So he guarantees to himself that he only plays the game once a month. However, Jack really loves playing game and hates programming, he wants to maximize the time he can spend on the game without breaking his promise.

Input Format:
The input consists of multiple test cases.
Each test case starts with a number N (0 < N <= 100,000) in a single line, the number of castles and Koopas. There are two lines following and each contains N numbers.
The first line is N numbers, T[i] (0 < T[i] <= 100) for Super Mario to conquer castle i.
The second line is N numbers of P[i] (-1 <= Pi < N), the castle (0-based) in which the Parent of each Koopa resides.
-1 means that there is no parent for him, and the last number will always be -1, since King Koopa has no Parent Koopa. The input ends with 0(zero), which should not be processed.

Output Format:
Output the maximal time Jack can play in a single line for each test case.

Sample Input:

5
1 2 3 4 5
4 4 4 4 -1
5
2 2 2 2 2
1 2 3 4 -1
9
1 1 1 1 1 1 1 1 1
6 6 6 7 7 7 8 8 -1
0

Sample Output:

12
10
8

Added by:	Prasanna
Date:	2007-10-08
Time limit:	10s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	NITT Local Contest 07 [ZJU inc constrts]

SPOJ Problem Set (classical)

1880. Hanoi Calls

Problem code: HANOICAL

Theory:

Towers of hanoi is an arrangement consisting of three pegs and N discs of radius 1 to N.
Each peg can hold zero or more discs, but at any point of time, the radius of the discs must be in decreasing order from bottom to top.
A move consists of moving the topmost disc from one peg to another. After the move, the decending order property of pegs must hold.

Traditional problem is: If all discs are stacked up on peg#1, how many moves will it take to move all the discs to peg#2?
Recursive solution: Noting that for disc N to move, from peg #a to peg #b, all discs of size 1 to N-1 must be in peg #c. Hence there is exactly one minimal way to move the discs. After disc N has moved, all pegs from #c must be moved back to #a. If moves(N) denote the number of moves required to transfer N discs between two pegs (both sorted configuration), then moves(N) = moves(N-1) + 1 + moves(N-1); Solving the recurrence yields moves(N) = 2^N -1; The idea i am trying to share is that, there is exactly one such move sequence.

Now the problem is that given any initial configuration of the discs, and any final configuration, Can you tell me the minimal number of moves required to change it from initial to final configuration?

Input Format:
The input file consists of multiple testcases.
The first line of each testcase contains one integer, N (1 <= N <= 30)
The second line of each testcase contains N integers, each one of which will be between 1 and 3. The i-th integer tells you the peg number at which disc of radius i is present in the initial configuration.
The third line contains a similar specification for the final configuration.
Input terminates with a line containing a single zero, which must not be processed.

Output Format:
For each testcase print one line containing a single integer, which is the minimal number of moves to make the transfer.
Testdata:
100 testcases

Sample Input:

Sample Output:

15
6
14

Output Explanation:
TestCase#1:
This is the moves(4) = 2^4 -1;
TestCase#2:

[peg1, peg2, peg3] = 
#0 [ {1}, {}, {3,2} ]
#1 [ {1}, {2}, {3}  ]
#2 [ {}, {2,1}, {3} ]
#3 [ {3}, {2,1}, {} ]
#4 [ {3}, {2}, {1}  ]
#5 [ {3,2}, {}, {1} ]
#6 [ {3,2}, {1}, {} ]

Added by:	Prasanna
Date:	2007-10-08
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	NITT ACM ICPC Local Contest 2007 [Self/Traditional]

SPOJ Problem Set (classical)

1881. Instruction Decoder

Problem code: ICODER

Mathews uses a brand new 16-bit instruction processor. (Yeah i am being sarcastic!). It has one register (say R) and it supports two instructions:

ADD X; Impact: R = (R + X) mod 65536
MUL X; Impact: R = (R * X) mod 65536
[For both instructions 0 <= X <= 65535]

Mathews sees a segment of code, but doesnot know what value the register had before the code was being executed. How many possible values can the register have after the segment completed execution?

Input Format:
The input file consists of multiple testcases.
The first line of each testcase contains one integer, N. (1 <= N <= 100,000).
The following N lines contain one instructions each.
Input terminates with a line containing N=0, which must not be processed.

Output Format:
For each testcase print one integer in a single line, denoting the number of different values the register can take after code execution.

Sample Input:

1
ADD 3
1
MUL 0
5
MUL 3
ADD 4
MUL 5
ADD 3
MUL 2
8
ADD 32
MUL 5312
ADD 7
MUL 7
ADD 32
MUL 5312
ADD 7
MUL 7
0

Sample Output:

Added by:	Prasanna
Date:	2007-10-08
Time limit:	3s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	NITT ACM ICPC Local Contest 2007 [Self]

SPOJ Problem Set (classical)

1960. Rectangles

Problem code: RECTANGL

You are given a set S of N points in the plane and must count the number of distinct axis-parallel rectangles whose four vertices all lie in S (that is, count those rectangles which have two sides parallel to the x-axis, and the other two sides parallel to the y-axis).

Input

The first line of the input is N (1 ≤ N ≤ 250000), the number of points in S. N lines then follow, where the i-th line is of the form "x_i y_i", giving the coordinates of a point (x_i, y_i) in S. All given points are distinct, and all coordinates fit into a 32-bit signed integer.

Output

Your output should consist of a single number, the number of distinct axis-parallel rectangles whose four vertices all lie in S, followed by a newline.

Example

Input:
6
-1 0
-1 1
0 0
0 1
1 0
1 1

Output:
3

Added by:	Jelani Nelson (Minilek)
Date:	2007-10-25
Time limit:	1s-30s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	MIT Individual Contest 2007

SPOJ Problem Set (main)

1961. Roman Roads

Problem code: ROMANRDS

Some 2000 years ago the Roman Empire covered a large part of Europe including the entire coast of the Mediterranean. The transportation network of that empire consisted of roads and sea routes (the two are considered equivalent and simply called roads for this problem). Each road connected exactly two cities and the road network was such that every city can be reached from Rome. However, building this network required resources (cobblestone and buoys) proportional to the total length of the network. In order to cut down on building costs and maintainance and spend the rest of the money on wine, the empire built the cheapest possible network.

Additionally, each road had a single signpost that listed all of the other roads it connected to (at any of its two cities). There were N roads in the empire labeled 1, 2, ..., N. It is believed that a traveller once travelled all roads and for each road wrote down the numbers on its signpost, thus making a map.

2000 years later a young archaeologist found something that looks suspiciously like that map. Your job is to write a program that determines if this can really be a map of the Roman empire and for each road output the two cities it connected. Note that roads in a valid map are always between two distinct cities.

(Disclaimer: The description of the transportation network is for this problem only and may not necessarily be what the Roman Empire actually did. Do not cite this in your history papers: I made it up.)

Input

The first line of input contains N, 1 ≤ N ≤ 500. Each of the next N lines contains a space-separated list of integers. The i-th of these lines describes the "roads" that connect to "road" i. The first number on the line specifies the number of those "roads", d_i, and the following d_i numbers specify their labels.

Note that although at this point we don't know if the map is valid, the input is consistent, i.e. if a road x is on the signpost of y, then y will be on the signpost of x. (Otherwise the archaeologist would know this is not a Roman map right away).

Output

If the input cannot describe a valid map according to the description, output "NO" on the first (and only) line of output.

Otherwise, output "YES" and on each of the next N lines, write two integers separated by space, the numbers of the two cities that the road connected. City labeling is up to you with the only restriction that all city labels must be integers between 1 and M, where M is the total number of cities. Of course, a city can only have one label.

Note that since we don't know the actual locations of the cities or whether the roads were straight, we have no idea what the total cost of the network might have been. The archaeologist is willing to accept any map for which she can't determine if there is a cheaper network without knowing the actual costs. It is assumed that each road had some positive cost.

Example

Input:
3
2 3 2
2 1 3
2 2 1

Output:
YES
1 3
4 1
1 2

Added by:	Jelani Nelson (Minilek)
Date:	2007-10-25
Time limit:	30s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	MIT Individual Contest 2007

SPOJ Problem Set (main)

1962. Circles

Problem code: CIRCLES

Little Gary plays the following video game. Circles pop up on the screen and disappear from it. When the screen flashes, Gary can draw a straight line on the screen and win as many points as there are circles intersected by the line. As a born-to-be-winner, Gary wants to maximize his score. Please, help him, and write a program that will determine the maximum number of points he can win each time the screen flashes.

Input

The first line of the input contains M (1 ≤ M ≤ 1000), the number of events during the game. The next M lines contain descriptions of the events, one per line. They can be in one of the following three formats:

1 x y r
, representing a circle of radius r popping up with the position of its center at (x, y) in the plane

2 i
, representing a circle i disappearing, where circle i is the ith circle that popped up since the beginning of the game; and

3
, representing the screen flashing.

x, y, and r are real numbers with at most two decimals, -10⁶ < x, y, r < 10⁶, r > 0.

Notes:

A line intersects a circle if it has at least two common points with it.
At any time, no two Circles on the screen have a common point.
At any time, there is no line that "touches" more than two circles (a line touches a circle if they have exactly one common point).
At any time, there are no more than 100 circles on the screen.
Each i determines a circle that is on the screen at the moment of removal.
No circle is removed twice.

Output

Each time the screen flashes, write an integer to a separate line, which is the maximum number of circles Gary can intersect.

Example

Input:
9
1 3.00 0.00 1.00
1 -2.00 0.00 1.00
3
1 2.00 3.00 1.50
3
1 2.00 -4.00 1.00
3
2 3
3

Output:
2
2
3
2

Added by:	Jelani Nelson (Minilek)
Date:	2007-10-25
Time limit:	30s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL

SPOJ Problem Set (classical)

1963. Image Projections

Problem code: IMGPROJ

Given an image I with N columns and M rows, a diagonal projection is the vector (d₁, d₂, ..., d_M+N-1) where d_i = Σ_x+y-1=i I(x,y). Here I(x,y), 1 ≤ x ≤ N, 1 ≤ y ≤ M, is the image intensity (a non-negative integer less than 256) at column x and row y.

You are given a set of images and you are asked to find the diagonal projection for each of them.

Input

The first line of input contains a positive number, the number of images that follow. For each image there is a line with N and M. The following M lines describe one row each starting from row 1. A row is described in run-length encoding by pairs of numbers separated by spaces. The first number in each pair is the length of the run and the second number is the image intensity. Obviously, for each row, the run lengths add up to N. As in the example input, there is a blank line between each two consecutive images and before the first one.

The number of test cases is at most 10. The width of each image is less than 10⁹ and the height is less than 10³. Additionally, the total size of the input does not exceed 4 MB.

Output

For each image you should output one line, the diagonal projection for the image in run length encoding. The number of output lines should be the same as the number of images in the input. All the numbers on a line should be separated by exactly one space.

When encoding the output in run-length encoding, the runs should be as long as possible, i.e. no two consecutive runs should have the same intensity value.

Example

Input:
2

3 3
1 1 1 2 1 3
1 1 1 2 1 3
1 3 1 2 1 1

3 2
3 1
3 1

Output:
1 1 1 3 1 8 1 5 1 1
1 1 2 2 1 1

Added by:	Jelani Nelson (Minilek)
Date:	2007-10-25
Time limit:	30s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	MIT Individual Contest 2007

SPOJ Problem Set (main)

1964. Tree cut

Problem code: MMCUT

You are given a tree (a connected, acyclic graph) along with a set of commodities, i.e. pairs of vertices, (s₁,t₁),...,(s_m ,t_m) (s_i ≠ t_i). A multicut is a set of edges that when removed disconnects s_i from t_i for all i. There is a unique path P_u,v between every pair of vertices u,v in a tree, and the max-cost of a multicut S is max_i |S ∩ P_{s_i, t_i}|. You will be given a rooted tree of height 1 and a set of commodities and must return the minimum possible max-cost over all multicuts.

Input

The first line of the input is "N M" (1 ≤ N, M ≤ 100000), where N is the number of vertices in the tree and M is the number of commodities. All vertices are numbered 0, ...,N-1, and the root has label N - 1. M lines then follow, where the ith line is "s_i t_i", representing a commodity (s_i, t_i) where s_i ≠ t_i. Commodities are distinct: neither (s_i, t_i) = (s_j, t_j) nor (s_i, t_i) = (t_j, s_j) will hold when i ≠ j.

Output

Your output should consist of a single number, the minimum possible max-cost of a multicut, followed by a newline.

Example

Input:
10 2
0 5
4 8

Output:
1

Added by:	Jelani Nelson (Minilek)
Date:	2007-10-25
Time limit:	30s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	MIT Individual Contest 2007

SPOJ Problem Set (main)

1965. Set Cover

Problem code: SETCOV

In the set cover problem there is a collection C = {S₁, ...,S_m} of subsets of the universe [n] = {0, ...,n-1}, and one must find a minimum-sized subcollection of C that still covers [n] (it may be the case that S_i and S_j contain the exact same elements for some i ≠ j). A path of length r is a graph on r+1 vertices v₀, ...,v_r where v_i has an undirected edge to v_i+1 for i = 0, ...,r-1 (these are the only edges). A set cover instance I is said to be path-realizable if there exists a mapping from I to a path of length m where the S_i are mapped to edges in the path and each i in [n] is mapped to a pair of (not-necessarily distinct) vertices s_i, t_i on the path such that the edges lying between s_i and t_i correspond exactly to the sets of C that contain i. Two sets S_i,S_j must be mapped to different edges on the path if i ≠ j. You will be given a set cover instance that is guaranteed to be path-realizable and should output the size of a minimum-sized subcollection of C still covering [n].

Input

The first line of the input is "N M" (1 ≤ N, M ≤ 300), where N is the size of the universe and M is the number of sets S_i in the collection of subsets of {0, ...,N - 1}. What follows are M groups of lines. The ith group starts with one line containing |S_i|, the size of the ith subset. If |S_i| = 0, the current group of lines ends. Otherwise the next line is a space-separated list of the elements contained in S_i.

Output

If [n] cannot be covered by a subcollection of C then you should output -1, followed by a newline. Otherwise, your output should consist of two lines. The first line is the size of a minimum-sized set cover. The second line is a space-separated list of the 0-based indices of the sets in an optimal set cover.

Example

Input:
3 4
0
2
2 1
2
1 0
0

Output:
2
1 2

Added by:	Jelani Nelson (Minilek)
Date:	2007-10-25
Time limit:	30s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	MIT Individual Contest 2007

SPOJ Problem Set (main)

1966. Ski Valley

Problem code: SKIVALL

The Society of Sport of New Hampshire has decided to build a new attraction in White Mountains. For the first time, the world will see a ski-valley, a ski path that goes downhill then uphill. They believe that skiers can gain enough speed from going down in the first part in order to climb up the second part. To maximize the joy of visitors, they want to find the longest such path.

To simplify calculations, they approximate the mountain terrain with a matrix of square fields and obtain the height of each field from the New Hampshire Geographical Institute. A ski-valley is a sequence of neighboring fields, such that height of fields only decreases along the sequence until some point, and then it only increases until its end. No field appears more than once in a ski-valley. Two fields are neighbors if they share a common edge. The length of a ski-valley is the number of fields in its sequence.

More technically, the terrain is an M x N matrix of fields, where (i, j) denotes a field in the ith row and jth column, and h(i, j) denotes its height. A ski-valley is a sequence (x₁, y₁), (x₂, y₂), ..., (x_l, y_l), such that:

for any i (1 ≤ i ≤ l-1), either x_i = x_i+1 and |y_i - y_i+1| = 1, or y_i = y_i+1 and |x_i - x_i+1| = 1 (neighbors rule)
if i ≠ j (1 ≤ i, j ≤ l), then either x_i ≠ x_j or y_i ≠ y_j (no repeating rule), and
There exists a k (1 ≤ k ≤ l), such that h(x₁, y₁) > h(x₂, y₂) > ... > h(x__k-1, y__k-1) > h(x_k, y_k) < h(x__k+1, y__k+1) < ... < h(x_l, y_l) (down-up rule).

The length of such ski-valley is l.

They hire you, a reputable programmer, to write a program that will find a ski-valley of maximum length. If there are multiple ski-valleys with the same (maximum) length, you can choose any of them.

Note: Yes, they were not cautious and also allowed a ski-valley to bo only downhill or only uphill, but your job is only to adhere to the specification they gave you!

Input

The first line of the input contains M and N (1 ≤ M, N ≤ 60), respectively, separated by a space character. Each of the next M lines contain N numbers, such that the jth number in the ith line represents h(i, j) (-10⁶ ≤ h(i, j) ≤ 10⁶). No two fields in the terrain are of the same height. Numbers on a line are separated by a space character.

Output

In the first line of the output, write a single number l_max, which is the maximum length of a ski-valley. In the next l_max lines write a description of any ski-valley of that length. In each of the lines, write two integers separated by a space character, such that numbers x_i and y_i in the ith line represent (x_i, y_i), the ith field in the ski-valley.

Example

Added by:	Jelani Nelson (Minilek)
Date:	2007-10-25
Time limit:	30s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	MIT Individual Contest 2007

SPOJ Problem Set (classical)

1991. Another Continuous Fractions Problem

Problem code: ACFRAC

The problem description is the same as the problem CFRAC and CFRAC2.

Input & Output

Multiple test cases, a single line with a single uppercase character C indicates the end of the input. The number of test cases will be less than 1000.

For each test case:

The first line of the input contains a single uppercase character A or B.A denotes that the input following character A and output format of this test case is the same as problem CFRAC, otherwise the input following character B and output format of this test case is the same as problem CFRAC2. But please pay attention that: the width and the height of the image after the character B will not appear in the input; the original fraction will not appear in the output of the test case of type A.

The example will make everything clear.

Example

Input:
A
75 34
B
..........1......
2.+.-------------
............1....
....4.+.---------
..............1..
........1.+.-----
................1
............5.+.-
................1
C

Output:
Case 1:
..........1......
2.+.-------------
............1....
....4.+.---------
..............1..
........1.+.-----
................1
............5.+.-
................1
Case 2:
75 34

Added by:	[Trichromatic] XilinX
Date:	2007-11-01
Time limit:	15s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	XX Colombian National Programming ACM 2006, test data by Blue Mary

SPOJ Problem Set (classical)

2000. Boxes (Hard)

Problem code: BOX

There are n boxes on the circle. The boxes are numbered from 1 to n in clock wise order. There are balls in the boxes, and the number of all the balls in the boxes is not greater than n.

The balls should be displaced in such a way that in each box there remains no more than one ball. In one move we can shift a ball from one box to one of it's neighboring boxes.

Write a program that: reads from the standard input the number of boxes n and the arrangement of balls in the boxes, computes the minimal number of moves necessary to displace the balls in such a way that in each box there remains no more than one ball, writes the result in the standard output.

Input

The first line of the input file contains an integer t representing the number of test cases. Then t test cases follows. Each test case has the following form:

The first line contains one positive integer n - the number of boxes
The second line contains n nonnegative integer separated by single spaces. The i-th number is the number of balls in the i-th box.

Output

For each test case, output one nonnegative integer - the number of moves necessary to displace the balls in such a way that in each box there remains no more than one ball.

Example

Input:
1
12
0 0 2 4 3 1 0 0 0 0 0 1

Output:
19

Note

There are two input files.

In the first input file, t=19, n<=1000, time limit=0.5 second;

In the second input file, t=3, n<=200000, time limit=15 seconds.

Warning: large input/output data, be careful with certain languages

Added by:	[Trichromatic] XilinX
Date:	2007-11-02
Time limit:	0.5s-15s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	POI III, stage 3; Special thanks to Lei Huang

SPOJ Problem Set (classical)

2002. Random Number Generator

Problem code: RNG

LoadingTime got a RNG (Random Number Generator) from his classmate several weeks ago. And he spent a lot of time study it. He found that RNG can generate a real number in range [-S,S] by executing following steps. First RNG generates n integer X₁..X_n, the sum of which is equal to S. Then for each X_i, it generates a real number in range [-X_i,X_i] randomly. The output (a real number) of RNG will be the sum of the N generated real numbers. LoadingTime noticed that the distribution of the output was very interesting, and he wanted to know: for given N and X, what's the probability that the generated number is in range [A,B]. Could you help him?

Input

The first line contains an integer T representing the number of test cases.

For each test case, the first line contains three integers N, A, B(1 ≤ N ≤ 10, -100 ≤ A ≤ B ≤ 100) In the second line of the test case, you are given X₁...X_n(1 ≤ X_i ≤ 10).

Output

For each test case, print a line contains a real number representing the probablity as the problem required. It must be printed with exactly nine decimal places.

Example

Input:
5
1 -100 100
10
1 10 90
10
1 -20 5
10
2 -20 5
5 5
5 -5 10
1 2 3 4 5

Output:
1.000000000
0.000000000
0.750000000
0.875000000
0.864720052

Added by:	Bin Jin
Date:	2007-11-03
Time limit:	1s
Source limit:	10000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C++ 4.0.0-8
Resource:	www.test-the-best.by

SPOJ Problem Set (algo_s3)

2005. Minus Operation

Problem code: MINUS

There are n integer numbers listed in one line. Every time you can arbitrarily choose two neighboring integers, kick them out and write down the result of the first number subtract the second number instead. Now, you want to get number m after you perform this operation n-1 times.

Input

Multiple test cases, the number of them is given in the very first line.

For each test case:

The first line contains two space-separated integers n(1<= n <=100) and m(-500<= m <=500). n lines follow, each contains a single integer (in the range [0,100]) denotes the original numbers.

Output

For each test case:

You should output n-1 lines, each contains a single integer p_i, which denotes that you are to wipe the p_i-th and (p_i+1)-th number in the current sequence and use their substraction instead. Each line of your output should not have any leading or trailing white spaces.

You may assume that there is always a valid solution to each test case in the input file. If there are multiple solutions, any of them will be accepted.

Print a blank line after each test case.

Example

Input:
1
5 4
12
10
4
3
5

Output:
2
3
2
1

Added by:	[Trichromatic] XilinX
Date:	2007-11-03
Time limit:	10s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	C++ 4.3.2 C++ 4.0.0-8 JAVA
Resource:	description by Blue Mary; standard program and test data by Zhou Yisu

SPOJ Problem Set (classical)

2006. Load Balancing

Problem code: BALIFE

SuperComputer Inc. have built a super-fast computer server consisting of N hyper-scalar lightning-fast processors Beta 007. These processors are numbered from 1 to N and are used to process independent jobs. Every new incoming job is assigned to an arbitrary processor. Sometimes, a processor may be assigned too many jobs while other processors have a relatively light load (or even wait idly). In that case, the whole system undergoes rebalancing.

Rebalancing proceeds in rounds. In each round, every processor can transfer at most one job to each of its neighbors on the bus. Neighbors of the processor i are the processors i-1 and i+1 (processors 1 and N have only one neighbor each, 2 and N-1 respectively). The goal of rebalancing is to achieve that all processors have the same number of jobs.

Given the number of jobs initially assigned to each processor, you are asked to determine the minimal number of rounds needed to achieve the state when every processor has the same number of jobs, or to determine that such rebalancing is not possible.

Input file specification

The input file consists of several blocks. Each block begins with a line containing a single number N(1<= N <=9000) - the number of processors. N numbers follow, separated by spaces and/or end of line characters. The i-th number denotes the number of jobs assigned to the i-th processor before rebalancing. There is a blank line after each block. The last block is followed by a single number -1 on a separate line (which should not be processed).

Output file specification

For each block in the input file, output the minimal number of rounds needed to rebalance loads for all the processors. If it is not possible to rebalance jobs so that each processor has the same number of jobs, output -1.

Example

Input file:
3
0 99 3

2
49 50

8
16 17 15 0 20 1 1 2

10
0 0 100 0 0 0 0 0 0 0

-1

Output file:
34
-1
23
70

Added by:	[Trichromatic] XilinX
Date:	2007-11-03
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	IPSC 2002

SPOJ Problem Set (classical)

2007. Another Very Easy Problem! WOW!!!

Problem code: COUNT

Background

This problem is somewhat easier than the problem A Very Easy Problem! because of the super long time limit...

Description

Assurance Company of Moving (ACM) is a company of moving things for people. Recently, some schools want to move their computers to another place. So they ask ACM to help them. One school reserves K trucks for moving, and it has N computers to move. In order not to waste the trucks, the school ask ACM to use all the trucks. That is to say, there must be some computers in each truck, and there are no empty trucks. ACM wants to know how many partition shemes exists with moving N computers by K trucks, the ACM ask you to compute the number of different shemes with given N and K. You needn't care with the order. For example N=7,K=3, the the following 3 partition instances are regarded as the same one and should be counted as one sheme: "1 1 5","1 5 1","5 1 1". Each truck can carry almost unlimited computers!!

Input

Each line of the input contains two postisive integer N (1<=N<=5000) and K(1<=K<=N).Input is terminated by a line with N=K=0(this case should not be processed).

Output

For each line, output the number of different partition sheme. To avoid big integers, you may output the answer modudo 1988.

Example

Input:
1 1
7 3
0 0

Output:
1
4

Added by:	[Trichromatic] XilinX
Date:	2007-11-03
Time limit:	21s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Time limit: 1000 Years! Memory limit: 2000 GB! Acc%: 100%!

SPOJ Problem Set (classical)

2008. Dab of Backpack

Problem code: BACKPACK

One day Blue Mary goes to a nearby supermarket to buy some goods. She has a backpack, whose capacity is V-Max. She finds that there are many goods in the market, each has a volume V_i(it will always be a multiple of 10 and less than 10000) and an importance C_i(1<= C_i <=5). Since she has almost unlimited money, the only problem she is to solve is how to choose goods such that the total volume won't exceed the capacity of the backpack and the sum of the product of the volume and the importance of each good is maximum. To be an excellent mathematician, she comes up with the answer quickly, and now she wants you to do a harder task. There are two kinds of goods: main goods and attachments. If you want to buy an attachment you must buy its main good before.

Input

Multiple test cases, the number of them is given in the very first line.

For each test case:

The first line contains two space-separated integers V-Max (1<=V-Max<=32000) and the number of the goods N (1<=N<=60). N lines follow, each contains three space-separated integers V_i, C_i and a integer u. If u is not 0, this good is an attachment of good u(as the order in the input file).

To make the problem not too difficult, Blue Mary tells you that:

(A) An attachment won't have any attachments which belong to it.

(B) A main good will always have less than 3 attachments.

Output

For each test case:

The first and the only line contains a single integer denoted the answer.

Example

Added by:	[Trichromatic] XilinX
Date:	2007-11-03
Time limit:	3s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Based on a Problem from Chinese National Olympiad in Informatics in Province 2006

SPOJ Problem Set (classical)

2009. Cryptography

Problem code: CRYPTO

Your task is to work as a cryptographer for some time, the reason is ...

Blue Mary has set a problem using English. Since the problem is too easy and it will be boring when solving it, she has deleted all the whitespaces and punctuations in the original problem description, and lowercased all the capital latin letters. Then, she randomly chose a permutation of the English lowercase letter alphabet, and then used the corresponding letters in place of the letters in the original text.

The encrypted text can be downloaded here.

There is no example for this problem.

Blue Mary's note: some tricky test cases were added on Nov. 25th, 2007 and the time limit has been changed. Programs have been rejudged and some "accepted" solutions got Wrong Answer. However, this problem can still be solved by quite clean code with length less than 1KB.

Added by:	[Trichromatic] XilinX
Date:	2007-11-03
Time limit:	1s-11s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: C99 strict ERL JS
Resource:	Sadly, the ability to make a simple problem difficult to understand is seldom considered a talent.

SPOJ Problem Set (main)

2019. The Rolling Ball

Problem code: ROLLBALL

Rolling Ball

Problem

A solid spherical ball of radius R rolls without slipping on the inside surface of a fixed cone, whose tip points downward. The half-angle at the vertex of the cone is u. Initial conditions have been set up so that the ball travels around the cone in a horizontal circle of radius l>R, with the points on the ball that touch the cone tracing out a circle on the ball. Determine the radius of the circle of these contact points, if you want the sphere to travel around the cone as fast as possible.

The Input

Each line of input has integers l (R < l <= 1000000) R (0 < R <= 1000) and u (0 < u < 90) given in degrees.

The Output

For each line of input, output the radius of the circle of the contact points, round to integer.

Sample Input

220000 100 29

Sample Output

Problemsetter --- Wu, Xiaogang

Added by:	Chen Xiaohong
Date:	2007-11-06
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL

SPOJ Problem Set (classical)

2021. Moving Pebbles

Problem code: PEBBMOV

A Game of Moving Pebbles

Problem

Two players play the following game. At the beginning of the game they start with n (1<=n<=100000) piles of stones. At each step of the game, the player chooses a pile and remove at least one stone from this pile and move zero or more stones from this pile to any other pile that still has stones. A player loses if he has no more possible moves. Given the initial piles, determine who wins: the first player, or the second player, if both play perfectly.

The Input

Each line of input has integers 0 < n <= 100000, followed by n positive integers denoting the initial piles.

The Output

For each line of input, output "first player" if first player can force a win, or "second player", if the second player can force a win.

Sample Input

3 2 1 3

Sample Output

first player

Problemsetter --- Chen, Jiahong

Added by:	Chen Xiaohong
Date:	2007-11-06
Time limit:	5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6

SPOJ Problem Set (main)

2022. Truth Or Lie

Problem code: TRUTHORL

Truth Or Lie

Problem

Suppose you have m yes or no questions that you want to ask n people. You are allowed to ask each person exactly two different questions. He/she will answer exactly one of them correctly and one of them incorrectly, you don't know which is a correct answer and which is an incorrect one. Given their answers, determine the number of combinations of answers to the m questions that can still be correct (i.e., no contradictions).

The Input

First line is the number of inputs. For each set of input, start out with a line of n<=10000 and m<=200, followed by n lines. The i-th line has four integers a b c d. It means that the answer given by the i-th person for question a is b, and for question c is d. Moreover, the answer "1" means yes, and "0" means no.

The Output

For each line of input, output "No Inference" if the answers do not help you eliminate any wrong combination of answers or the number of combinations of possible answers is 0, otherwise output the size of the set of combinations of answers still possible.

Sample Input

Sample Output

No Inference
2

Added by:	Michał Małafiejski
Date:	2004-05-01
Time limit:	10s
Source limit:	50000B
Cluster:	Cube (Intel Pentium G860 3GHz)
Languages:	All
Resource:	Douglas Adams, The Hitchhiker's Guide to the Galaxy

Added by:	Adam Dzedzej
Date:	2004-05-01
Time limit:	6s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: NODEJS PERL 6

Added by:	Adrian Kosowski
Date:	2004-05-01
Time limit:	7s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	BF ICK WSPC

Added by:	Darek Dereniowski
Date:	2004-05-10
Time limit:	5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: NODEJS PERL 6
Resource:	DASM Programming League 2003 (problemset 11)

Added by:	Konrad Piwakowski
Date:	2004-11-16
Time limit:	17s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: NODEJS PERL 6
Resource:	DASM Programming League 2004 (problemset 3)

Added by:	Patryk Pomykalski
Date:	2004-05-22
Time limit:	1s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: NODEJS PERL 6

Added by:	Łukasz Kuszner
Date:	2004-06-01
Time limit:	4s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: ERL JS NODEJS PERL 6
Resource:	PAL

Added by:	Neal Zane
Date:	2004-06-08
Time limit:	9s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: NODEJS PERL 6
Resource:	Neal Zane

Added by:	Michał Czuczman
Date:	2004-07-11
Time limit:	3s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: NODEJS PERL 6
Resource:	Swiss Olympiad in Informatics 2004

Added by:	Piotr Łowiec
Date:	2004-07-02
Time limit:	7s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All

Added by:	Krzysztof Kluczek
Date:	2004-12-09
Time limit:	17s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 C99 strict CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	DASM Programming League 2004, problemset 4

Added by:	Tomasz Niedzwiecki
Date:	2005-01-22
Time limit:	8s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL

Added by:	Bogusław K. Osuch
Date:	2005-04-14
Time limit:	15s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 C99 strict CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	:P

Added by:	Duc
Date:	2005-04-28
Time limit:	19s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: NODEJS PERL 6
Resource:	Based on a problem from acm.uva.es

Added by:	Paweł Dobrzycki
Date:	2005-04-29
Time limit:	2s
Source limit:	8196B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: NODEJS PERL 6
Resource:	IV Podlasian Contest in Team Programming

Added by:	Tomek Czajka
Date:	2005-05-03
Time limit:	7s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: NODEJS PERL 6
Resource:	Purdue Programming Contest Training

Added by:	Duc
Date:	2005-05-25
Time limit:	20s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: NODEJS PERL 6

Added by:	Le Trong Dao
Date:	2005-06-08
Time limit:	50s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: NODEJS PERL 6
Resource:	Mr.Tran Minh Quan

Added by:	Noszály Csaba
Date:	2005-06-10
Time limit:	7s
Source limit:	7777B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All
Resource:	Folklore

Broad gauge (Spain):	1674 mm
Broad gauge (Portugal):	1665 mm
Broad gauge (Ireland):	1600 mm
Broad gauge (Finland):	1524 mm
Broad gauge (former USSR):	1520 mm
Standard gauge:	1435 mm
Narrow gauge (meter gauge):	1000 mm

Archives of the Sphere Online Judge

classical problemset

Preface

Table of Contents

SPOJ Problem Set (classical)

1. Life, the Universe, and Everything

Problem code: TEST

Example

SPOJ Problem Set (classical)

2. Prime Generator

Problem code: PRIME1

Input

Output

Example

SPOJ Problem Set (classical)

3. Substring Check (Bug Funny)

Problem code: SBSTR1

Input

Output

Example

SPOJ Problem Set (main)

4. Transform the Expression

Problem code: ONP

Input

Output

Example

SPOJ Problem Set (classical)

5. The Next Palindrome

Problem code: PALIN

Input

Output

Example

SPOJ Problem Set (classical)

6. Simple Arithmetics

Problem code: ARITH

Input

Output

Example

SPOJ Problem Set (classical)

7. The Bulk!

Problem code: BULK

Input

Output

Example

SPOJ Problem Set (classical)

8. Complete the Sequence!

Problem code: CMPLS

Input

Output

Example

SPOJ Problem Set (classical)

9. Direct Visibility

Problem code: DIRVS

Input

Output

Example

SPOJ Problem Set (classical)

10. Complicated Expressions

Problem code: CMEXPR

Input

Output

Example

SPOJ Problem Set (classical)

11. Factorial

Problem code: FCTRL

Input

Output

Example

SPOJ Problem Set (classical)

12. The Game of Master-Mind

Problem code: MMIND

Input

Output

Example

SPOJ Problem Set (classical)

13. Hotline

Problem code: HOTLINE

Input

Statements

Questions

Language 1 Phrases	Language 2 Phrases
arlo zym	bus seat
flub pleve	bus stop
pleve dourm	hot seat
pleve zym	school bus

Added by:	Ivan Metelsky
Date:	2005-08-25
Time limit:	2s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: NODEJS PERL 6 PYTH 3.2.3 n
Resource:	NEERC Western Subregion QF 2004

Added by:	Sebastian Kanthak
Date:	2005-10-26
Time limit:	5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: NODEJS PERL 6
Resource:	ACM Pacific Northwest Regional Contest 2003

Added by:	Piotr Piotrowski
Date:	2004-11-08
Time limit:	13s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: JAR

Added by:	Lukasz Wrona
Date:	2004-12-29
Time limit:	3s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: NODEJS PERL 6

Added by:	Kashyap KBR
Date:	2005-12-08
Time limit:	8s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: NODEJS PERL 6

Added by:	Nguyen Minh Hieu
Date:	2005-12-20
Time limit:	2s
Source limit:	10000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 C99 strict CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	Romanian National Contest

Added by:	Nguyen Dinh Tu
Date:	2006-01-02
Time limit:	5s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: NODEJS PERL 6
Resource:	Tran Quang Khai

Added by:	Hoang Hong Quan
Date:	2006-01-05
Time limit:	18s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: AWK C++ 4.3.2 CLOJ ERL F# GO JS NODEJS PERL 6 PYTH 3.2.3 PYTH 3.2.3 n SCALA SED TCL
Resource:	BOI 2004

Added by:	Duc
Date:	2006-01-24
Time limit:	1s-4s
Source limit:	50000B
Cluster:	Pyramid (Intel Pentium III 733 MHz)
Languages:	All except: NODEJS PERL 6
Resource:	VII Polish Olympiad In Informatics 2000, stage III